Hi poppy, if the yoga is causing pain like that definitely don't do it, however you'll know you are recovering when you can do it without such pain iykwim?
I believe medically speaking it's harder on the body to be overactive. It can affect heart, muscle and bones quite badly. I don't think you'll get fat/ put on weight either but it's going to take a while for everything to even out and recover, balance out so to speak.
You will feel it within yourself when this starts to happen.
I do not ever have a weight issue when underactive, the opposite actually, and have learnt that keeping muscles in top condition, doing cardio and strength stuff helps to stay fit and improves the way my body used the thyroxine.
The only real issue anyone underactive has is making sure they're on the right level of thyroxine which often is got wrong by gps. The other thing which isn't general practice but I can vouch for as many here on mn can is that when on thyroxine you need to have good ferritin levels, b 12, Vit d and folate. It's not that hard to manage the b12 d and folate through diet and Vit d drops but the ferritin can need proper attention to get anywhere. I've been reading mns posting ferritin needs to be over 70 (50 is borderline, don't usually treat til a lot lower) but it is utterly my recent experience. Personally I think it's simply down to muscles need to have good iron levels to recover and women can loose through menstruation.
You are not underactive though and not everyone swings that way, the anxiety side of things is horrid but will all get better as you feel better and muscles start behaving.