So I know if I cut my hair and started T, I could easily pass. Like I have said before, I have very large hands, strong jawline, etc. But, I am only about 5'3" or 5'4". I know height shouldn't matter but I feel like it does.

Since I am still young, if I started T soon, could it maybe make me taller, since I haven't stopped growing?

Little help on the height thing please 

Wear Docs...  My Doc Martens give me like two inches.  Spiking your hair can make you look taller but you can also end up looking like you're trying to look taller, hehe   As far as I know T can't affect anything about your bone structure, but I'm no expert.

If you're a teen, there's a chance you may grow taller. Most people's growth plates fuse somewhere between the ages of 18 and 22; if they haven't fused yet then you may grow a little bit.