Hashimoto's is soooo frustrating!!! I, too, came down with it at 19 and have struggled with it for the last 11 years. It IS possible to lose weight, but you have to be aware of several factors at play.
First, it's really wise to go gluten free. Hashimoto's is an autoimmune disease, and gluten is a trigger - your immune system will attack both the gluten AND your thyroid because they're chemically similar. Y
My thyroid levels look fine (except for high antibodies, which reaffirm that I have Hashimoto's), but I've been feeling AWFUL for a few months!!! I finally gave my doctor a printout of thyroid symptoms with the ones I'm dealing with highlighted (at least half, even though my bloodwork says I'm fine). Switching medication from Synthroid/levothyroxine to Armour and liothyronine has helped immensely, but I'm still dragging and will be seeing an endocrinologist soon.
Good luck! Hope you feel better soon!