I have an underactive thyroid too, and I take 25mg of Eltroxin. When I first started taking them, GP told me to leave it at least 2 months before retesting. I takes about that time for everything to readjust to the medication. I think in most cases, a GP will wait 3 months to re-evaluate. In February of this year, my GP increased my dosage to 50mg, but believe it or not, I actually stopped ovulating once I started taking the 50mg. GP said it was possible the 50mg might have been too much for me, so I went back down to 25 and everything was fine again.
Anyway, I reckon you'll need to give it the two months at least. Hopefully things will settle down for you now that you're on the Eltroxin. The tiredness from having an underacive thyroid can be off the scale, as you may well know!! So at least you've caught it now