You have reason to be stressed out and upset. Just because they are not privy to that knowledge, doesn't mean it's not valid. You know, and it's fair, so start by giving yourself a break.
Your mom, for example, said she is ashamed you're her daughter. That's a fucked up thing to say. That being said, she's upset and you being empathetic to that, maybe you understand she doesn't really mean it. The rule should not be everybody "gets a break" here except you, so try not to be hard on yourself.
As for how it appeared to everyone else, it might've looked rude and maybe it technically was, but there are so many worse things. It feels wrong and painful now because you're still riding it out, but this will be a relatively minor thing years from now, if your parents are healthy, normal people.

I can't offer advice for how to actually communicate with your mom because I don't know how she is, or how you're approaching your discussions with her. Sometimes, as tempting as it is to want to explain yourself to the person, they only see it as you making excuses. Even though you might really just be wanting to build an understanding, that is really just how some people interpret things. That is my SO to a T, for example, and it's completely against my nature. If you have approached her and said, "I'm sorry for what I've done, it was wrong. I've learned, and I'd appreciate if you could give me a chance to improve myself going forward," and if your parents still want to hold it over your head, then it might just be that they're the ones being the problem. It might sound weird to a kid when those are the only parents they've ever known, but some parents are better than others. I don't know if that's the case here, but if it is, that's not your fault.

Also, I hope you have someone to talk to about your brother.