Hi Belle, we're in a similar boat, so here's my 10-pence worth fyi.
First, I just wanted to reassure you that irregular and extended bleeding is definitely one known side-effect of fibroids. I had exactly the same thing as you: non-stop bleeding which the doctor prescribed Provera for, then sent for an ultrasound (or rather, I demanded one). Anyway, the bleeding was shown to be because of problematic fibroids.
Like you, keeping my fertility is important, as I haven't yet had children. I am going to be getting a myomectomy, however, my specialist has put me on Zoladex (another HRT like Esmya) in order to shrink them before I get a myomectomy. There are limited ways of dealing with fibroids if you want to keep fertility, because some things like UFE are not recommended, and I understand that MRI-guided ultrasound is still an unknown quantity as far as fertility is concerned.
Esmya and Zoladex DO help shrink fibroids, but are both short-term solutions, because you cannot be kept on it indefinitely due to serious long-term side effects such as bone-density loss. They're generally prescribed in order to manage symptoms before surgery.
I imagine you'll be offered a myomectomy, but depending on where and how big your fibroids are it'll be laparoscopic or laparotic. I'm going to have to have laparotic, which will be fairly major surgery. You might be asked if you want a hysterectomy, but you should not feel pressured to consider it as an option unless there is a serious malignancy which needs addressing (but that is VERY rare, so don't worry yourself needlessly by looking up the worst-case possibilities online, believe me, it's not worth it or necessary, wait to hear back your ultrasound results.)
Finally, just want to reassure you that what you're going through is actually pretty common, so don't worry too much! Stress is bad for your health, and some people even think it plays a part in fibroid-growing hormone imbalance. (I don't know if it's true, but I DO believe stress is as bad for your mind and body as any illness). Like some other commenters here, I changed my diet to cut down and then out meat and dairy which are known to contain hormones. I have no idea if it'll help long-term, but I want to give my body the best chance to eventually have kids. Unfortunately fibroids can grow back after myomectomy, so I am trying to implement changes which are thought to help prevent hormone imbalance. So...yeah, that side of things is a personal choice, just do what you think is right for you.
But as far as surgery, insist on hearing ALL the options, and get a second professional opinion if you're still feeling unsure.
Sorry for the long reply, but I think we have lots of similarities in our cases, except I'm now nearly a year into this. Anyways, best of luck, and feel free to ask if you have any more questions.
xox Rosie