Hi Rachael,
Having read the replies below I would also suggest that you ask for a Thyroid Antibodies test, if this is positive then you have Autoimune Hypothyroidism which will need treating for ever and it is an important distinction.
I would also ask for Fertin, Folate,b12 and Vit D to be tested as these need to be high in range to assist with the absorbtion of the medication. They can also cause some similar symptoms if they are low.
If your TSH is truely 100 then it is going to take time. The protocol that your doctor should follow is to start off on a low dose of medication and slowly increase until your levels stabilise. He / She should be doing follow up blood tests every 6 weeks to ensure the levels start to come down for TSH and rise for T4 / T3.
I would ask for a copy from the recption of the results of every single test so you yourself have a record of your progression.
Doctors will not always do the extra tests, I am also registered on the Thyroid Uk website. They have some great downloads and symptom checklists as well as the best forum for support I have come across, this website is also recognised by the NHS. They also have some links for good private testing that will not break the bank if your doctor is reluctant to do the extra tests.
Take your medication an hour away from food, and four hours away from supplements with a full glass of water. If you get lots of side affects try taking it before bed.
When you go for the next set off blood tests do not take your medication in the morning or evening before as this can sometimes give false results. Also make sure you fast before and the appointment is as early in the morning as possible.
If the medication is making it worse you could try taking it every other day for a week then add in the other days, I had to do this every time I had a rise in medication. I would give it a good 4-6 months to really see if the medication is working. If not or your symptoms are no better insist on a referal to an endocrinologist.
Lots of people with hypothyroidism remove Gluten from the diet with some great results, it did not help me too much but I have manged to cut of bread, cakes and biscuits from my diet.
Good Luck and always ask questions on here or the Thyroid Uk site if you need support. Lots of us have been where you are and can offer understanding and support if you need it.