It can take some time before things start to level out properly.
I know it was between 5-6 weeks after RAI that I went hypo where my TSH was over 6.0.
Thats when I was started on a small dose of T4 med (25mcg every 2nd day).
Its normal for the tsh to be low for a while after RAI as most people dont know or havent had it explained to them that just prior to going hypo, that the thyroid tries one last time to try and 'fire up' to function and this can cause hyper symptoms with a rapid heartbeat.
After that episode which may last a few days...the thyroid then dies off.
As for your menstrual cycle, I cannot comment on that by experience as I went through early menopause but as with all hormones, I would say that it could be 'unbalanced' for a while. Ask your Doc and see what he/she says about it.
Other than that I would recommend seeing a Gyno and getting checked.
As for apetite, it took a long time for mine to come back and I dont eat like I used to prior to RAI when I was hyper.
Hope that helps.