That is indeed a sticky situation.
I'd suggest sitting down with her and letting her know what's running through your mind. Not pleading, or getting over emotional - but telling her that you really feel you need to find your identity and trying out the shirt going to help clarify things for you.
The horror stories in relation to chest binding refer to using things like compression bandages and tape. Those are the really dangerous methods of binding. Using a commercially available compression shirt? About as dangerous as a really tight sports bra.
Maybe you could suggest some sort of compromise? For example, you could offer to set a maximum time of wearing the shirt per day if she's worried extended use could harm your development.
I think she's going after your car because she feels as if she's losing control of you, and she's trying to gain some back. I think all parents do that when you get to a certain age. My Dad's favourite was that he was going to take my dizzy cap or rotor button! After he said that I started packing spares. He never actually did it though.. possibly because I know more about engines than he does

But seriously, the more you go behind your mom's back, the harder she's going to try to restrict you. I really think you two need to sit down and work out some way that you can express yourself, and she can be reassured that you aren't harming your development in any way.
I know it's probably not what you want to hear, but I think it's your best shot right now given you're still young and living at home.
Good luck!