I would gently suggest to your mom and brother that he visit a dermatologist about his face. Just say, "have you ever considered...?" and then let it go. Don't be pushy. My stepson had really horrible cystic acne and needed an Rx for a while. My nephew (just a little older than your brother) also had acne problems and always walks hunched over and wears a hat like he wants to hide/fold in on himself. He's SO painfully shy. He has no confidence outside auto mechanics and I wish he could see that he's a good, kind kid that people like, if he gives them a chance.
He doesn't need to be like you. My nephew isn't like his brother or his sister. And that's fine. What worries us more than what he wears is how he acts and we are concerned that he's just unable to present himself to others. He wants to go into the military but struggled to speak to the recruiter. I think he might have some agoraphobic tendencies like his mother and grandfather. It can be crippling. Maybe your brother has something like that going on beyond just being shy. Maybe he wears the jacket *because* it is snug and he has sensory issues.
For what it's worth, both my stepkids are often hermits when they are home in the evenings. I think it's just a way to decompress. I am an introvert in a family of extroverts. Sometimes I tell them to all go away because they are stressing me out. My DH recharges with people. I don't. Sometimes he has to go do his thing without me because I just can't do one more thing that involves being "on" for other people. Maybe your brother is the same on some level.
What you see as "tough love" may not be appropriate here. Teasing can be really hurtful. I'm not saying to baby him but there's "Would you like to go shopping with me?" vs "You look homeless in that jacket." It can be hard to be seen with someone who doesn't fit your mold and you feel judged on that behavior. Do you ever speak gently and encouragingly? "What do you want to eat, Bro?" maybe if it's said in front of the waitress to you, it will be a step toward ordering for himself.
Another thing - so what if his choices are "old". I am not really into comics or football or fashion, but I listen to the kids and try to understand their interests because it's important TO THEM. I'm never going to be a huge comics fan, but I can appreciate Green Lantern because I've listened to SS talk about it. Maybe rather than diss his music, give it a chance. Let him share with you.
It might also help your parents to speak to the school guidance office and get their take on his behavior and what might be done to help him. Being different is one thing. Hiding like that is something a bit more concerning. He may have other things that need to be treated and evaluated. Not being able to order at 15 would be a concern for me.