First of all, a big hug for you.
Secondly, shopping is really no big deal. Worse come to worse people think you're buying for a wife, girlfriend or other relative. I mean, I can't tell you how many times I've gone shopping in full male mode in department stores and other places, even Target and Wal-Mart. Nobody cares!!! You might find an occasional twit but most people don't really bother you. Goodwill is a cheap source for clothing. I also routinely scout the clearance rack at Kohl's and Macy's.
As for going out in public, take baby steps to build your confidence. Try a few accessories and ramping it up. See how you can get yourself to look more femme, whether it's hair removal, painting your nails, growing your hair, etc. You would be surprised.
Also, your local PFLAG chapter, if there is one near you, may have support group meetings. That can help.