It is good that your case is not very severe, your T4 and T3 being in the normal range, so you don't have to take more Methimazole (MMI) than just the one small pill per day. Was the test testing Total or Free T4 and T3? Usually they test Free T4 but sometimes only Total T3. [Since your numbers are not far off, I would think this has not been going on very long.]
There are several things you mention that I can identify with, mostly before I was diagnosed at age 60:
1. At age 38, while pregnant with my 3rd child, I was too tired to get off the couch. But I have always been too tired to go into business for myself.
2. Between the time I had my 0.01 results on a TSH test and the time I saw an Endocrinologist, I had my FreeT4 tested and shown to be 8.9, just a bit above the normal range (0.8-8.0). [I am going from memory, not rechecking my actual numbers]. The GP ordered an uptake scan, but said I didn't need meds at that time and to see him in 3 months. This was on a letter he sent me and the part about seeing him in 3 months was highlighted, but at the time, I thought it was crossed out, and didn't make the follow-up visit until about 6 months had passed. [mental confusion was also a symptom.] After the scan with iodine, I felt great. But I don't remember the specific outcome of the test.
3. When I was complaining about my symptoms, being tired, weight gain, etc. around age 45-50, my doctor wanted to try me on antidepressants, prescribing Paxil which made my sleep schedule erratic, and I developed an aggressive attitude with a very apathetic attitude as well. I stopped the Paxil and refused the next antidepressant. He finally persuaded me to take Prozac long enough for me to convince him it was not helping my symptoms. Just in the last year I was put on Wellbutrin, though, which helped a great deal, but then I still went through a time of increased depression so Zoloft was added to it. Within the month I was having much worse symptoms with it. My Wellbutrin dose was increased instead, I stopped estrogen treatment which was making me worse, and now I'm fine.
4. I had a lot of bladder infections, and vaginal infections that would appear to be bladder infections.
5. I had eczema on my legs which was treated with a cortizone type cream. I also had one episode of mouth sores. The doctor said it was "Johnson Disease" and gave me something for it that didn't really help much. I considered that I may not have been getting enough (hardly any) vitamin C, so I tried improving my intake and the mouth sores went away.
6. Up until age 38 I was usually very thin (exculding pregnancies) at 132 lbs, 5' 6" tall. From age 38 to 59 I gained 65 lbs. The weight gain was never dramatic, and it usually followed a weight loss. I would lose 5 lbs and gain back 10 through most of that time. In May 2008 I started a diet that emphasized healthful foods and actually increasing calories, if one were to count them at all. I lost about 12 lbs over 3 months, but I had turned 60 in July and had the TSH test at practically zero. At the end of the month, I also had a colonoscopy, which disrupted my diet and I started to regain the lost weight. The most I ever weighed was about 212 lbs. The MMI can make you gain weight, but more so if you have to take higher doses. Personally, I still think the diet I was on was good. It was to have 3 meals and 3 snacks per day. Each meal and snack was to have a glass of water, All meals and snacks except breakfast were to have a vegetable. All meals were also to include whole grains, protein, and fruit. Usually having the fruit as a dessert, but other sugar sweetened desserts could be eaten if you were not "comfortably satisfied". Artificial sweeteners were out, as was alcohol and any caffeine. I called it "the five finger diet" because you could count the foods and water on the fingers of one hand.
7. My eyes were never bulgy but I have had double vision since I was about 14 years old. One eye was operated on to fix the muscles when I was 17. When I was 30 I was having more problems and my vision was improved with prizms in the lenses of my glasses. The amount of prizms was increased from time to time after that. I got bifocals when I was 60, but the prizms were geared to distance vision and seemed to be wrong for close work that I did much of the time, including hours and hours of computer work. My eyes also got dry, etc. The double vision got much worse at the end of 2008 and I went to an eye specialist in 2009 who diagnosed the Graves' Disease. The endocrinologist my doctor referred me to could not see me until July so in May my doctor sent me to one who could see me right away. That was when I was put on MMI 30mg per day, half in the morning and half at night -- so that was 3 pills each time. I was given a beta blocker as well and instructed to stop it after one month and reduce the MMI to 2 pills each morning and each night, then to see him after the second month. Taking the MMI was always worse for me than the disease, according to how I felt, but my heart rate of around 130 beats per minute settled down.
Since then I have seen 3 more endocrinologists. After 2 years with the first, I refused the medication and cancelled my appointments. and had a pleasant summer. I was practically forced to go to an Endo again, so I went to the one my doctor had originally recommended. He was better, but the MMI still bothered me. I was started at 5mg 1xd then but increased to 2xd before I really began having a difficult time and was finally able to decrease the dose again. After the first decrease, my TSH shot up from zero to the middle of the normal range. The next time my TSH was above the normal range and the endo decreased the amounts again. He had me cutting my pills in half and taking 1.5 a day, then different amounts on different days of the week to allow for only a slight decrease in the weekly amount. After that the endo was more reluctant to allow any more decreases, but I decreased it myself and informed him later what I had done. He approved it retroactively because my TSH stayed in the normal range. I went off altogether in December 2013. I felt miserable because there was no more MMI to decrease and feel better. My endo would not prescribe supplements. My FT3 was very low and my FT4 was about mid-range. I went to Endo #3 but didn't get any help there either, except that Endo #2 refused to see me again. For that reason my new GP decided to treat me for hypothyroidism offering me several choices and I chose Cytomel, aka Liothyronine or L-T3) I did well on it for about 4-5 months adding Levothyroxine in the last 6 weeks until my TSH fell to zero again. Then I had to pick another Endo. I have seen him for a year now. He took me off the supplements; my TSH became normal, but I felt horrid again, until my GP put me on Wellbutrin which seemed to restore me back to normal until I started the estrogen treatment and got horrid PMS-like symptoms with a lot of nervous tension.
The bulging eyes comes from the autoimmune response in the disease and not from the thyroid itself. The auto-antibodies attack the same protein in the eye muscles as in the thyroid. For that reason RAI is not usually recommended if there is any sign of eye bulging. Sometimes they recommend surgery anyway. I refused either, having been first diagnosed before they recognized the association between RAI and worsening of the eye problems. I refused because I knew they could never restore my thyroid again and I never trusted them to supplement my thyroid hormones adequately afterwards.
I had a second eye muscle surgery in December 2009 which really didn't help at all because the surgeon did not allow for the fact that the previous surgery had already corrected my right eye to the greatest extent possible.
I am now 67, wear reading glasses with prisms all of the time. I drive, mostly locally, looking over the top of them and shutting one eye at a time. I also try to stay in the same lane of traffic most of the time, don't go on unfamiliar routes and park by driving straight through one spot to park in the facing one but with me facing out so I can drive out forward instead of having to back up.
I also learned from Linda here about the Acetyl-L-Carnitine which I have taken about 6-9 months. If I miss even one dose I notice more difficulty with my eyes and also with bladder control.
Even though I have no direct advice for you, I hope you can profit from my experience.