This may not be what you want to hear but I think you are both too young and too early in your hair loss to have a hair transplant. You are only 22, and you do not know how far or how fast you will progress. It is good you are on meds and I would suggest you stick with them for a while and see how you do for a longer period of time.
You can always do hair transplant later, but if you do it too early you will sacrifice your grafts too soon and may end up needing more surgery than you may want later on.