How to progress?
Buy your own stuff
That way, you don't need to worry about mum noticing something moving. You also get to pick something YOU like. After all, you're 16, she's probably around 40 - I wish I was 16, there's a metric tonne of clothing I'd love to wear, but I'm around 40.
As to your parents, if they love you, they'll love you even if they discover you're on the trans spectrum.
It's normal, it's not shameful, it's natural...your coming out could be the impetus they need to improve their opinions
Approximately 7% of people are on the trans spectrum, either wishing to transition or go no further than dressing in private. 7%... That's 1 in 153 people. How many people at your college? On your street - you are NOT the only one. Depending on where you live, there will be support groups, trans friendly clubs....give it a couple of years (so you're old enough to drink), and meet people.
Other advice I'd give my 16 year old self (but can't so I'll give it you): Grow your head hair but keep removing all body hair. Tell every boy/girlfriend - if they leave, they were never meant to be. One will stay, and they're the one.