if you're without a doubt going to use ace bandages anyways, I can't stop you. but it's really unsafe, even if it's only for a short period of time. wearing them for an hour is a lot better than wearing them for a whole day, but it still is risky. I mean, even tape is safer than ace bandages. pretty much everything is safer than ace bandages.
sorry, I'm not trying to be all preachy or whatever, but ace bandages just really aren't safe, especially if you've already got respiratory problems. is there any way you could get a proper chest binder? if your mom's supportive, and you could afford it, I'm sure she'd be willing to help buy you one. or if not, maybe just try wearing a large hoodie that helps conceal your chest?
I don't really know how the legal name/sex changing process works, but I'm sure that is possible.