I would advise against trying to start HRT while in the Navy. That can get you into alot more trouble than being trans. Discharge for transexualism is administrative, and not medical and is outlined in the Standards of Medical fitness. If you only have two years left just keep going. It may sound like a long time but you'll be OK. I know, because I've been there...recently.
If you feel like people know and may be outted it's important to contact Service Members Legal Defense Network (SLDN), they are great folks, and it does not cost anything.
As for the VA, they cover therapy, HRT, bloodwork. Some even have TG support groups.