Hi, I have hashimoto, so an underactive thyroid. The drugs are not in any way "bad" for you, you are just replacing the hormones your body does not produce, there is no need to worry about problems from side effects. What does affect your freediving is whether you manage to get your hormones well balanced with the drugs or not, as a underactive thyroid affects your whole body, and so does an overactive one. If you have too much of the hormones, you will notice it, if you don't have enough, you will notice, too. For most people, after some time, they achieve a good balance and feel normal and healthy. For some, it is a lot harder and never really back to normal. Problems with your thyroid will affect your freediving, as it affects things such as heartrate, circulation, how efficiently oxygen is metabolised, etc etc. It can take quite some time to get your body to be back in balance again, but you should be able to freedive fine, although you might notice that sometimes things are different (such as contractions consistently coming much earlier) and that may have to do with something going on with your hormone levels.
On the whole, you need a lot of patience when dealing with this. A great book to read is Mary J. Shomon: living well with hypothyroidism. I really recommend it, it gives you all the information no one else will! Good luck with it, don't worry, you can still enjoy freediving!
Anna
