I've been underactive and overactive during pregnancies. My thyroid levels always have leveled out right round the 5 month mark so I went off of meds. I was very concerned about being on PTU during pregnancy and nursing but the endocrinologist said it was alright. . Both of my children are very healthy and have no thyroid issues as of yet. Thankfully, I am now in remission but still considered to have Graves disease
One suggestion I have is to see a chiropractor. I just found this out recently and had no idea my spine played such and integral part of my health. I had a neck injury many years ago and shortly after that was diagnosed with thyroid disease. If there's any nerve interference with your C7 vertebrae, it can affect your thyroid levels. Had I known then what I know now, I wouldn't have had to go thru such a struggle. You don't have to have an injury to have compression on the nerves that run out of the vertebrae. By having your spine in proper alignment it allows your body to heal naturally. If you need a referral for a chiropractor, I go to one in Twinsburg that is awesome. I'm not sure where you're at so PM me if you'd like more info.
There may be other natural things you can try so you may want to do some research. I know a doctor will never tell you this but I've read some other posts on this website where women have had success going off of meds. Sorry I don't have more helpful info on this part but you may want to post again if you're interested in homeopathic approaches
Congrats on your pregnancy and good luck!