There is no “right” or “wrong” way to deal with your brother’s loss. Others here have given excellent answers. It’s not “wrong” to throw most everything away, but it’s also not “wrong” to want to keep it all. The problem is when one person’s idea of “right” gets to trump someone else’s (also perfectly reasonable) idea of “right.”
I think the quick rush to throw everything away is a hasty and rash thing, but then again, I’m a packrat. I still feel regret and anger at my mom, who basically gutted my dad’s possessions the day after he died, giving stuff away, throwing stuff away, and putting it on the curb. She gave away all my dad’s precious Army stuff, including his uniform, something my sisters and I would have loved to have had. We did reclaim his Army overcoat, but the rest of it was gone. It still pisses me off.
It wasn’t wrong for her to do that, if it was just her that was affected. But she (in her terrible grief and shock) tried to tell the rest of us that we were silly and foolish for caring about his stuff. That was wrong. I understand how she felt, but it was wrong to not take into account the feelings of others. Like others have said here, some compromise should be made.
One of the worst things that is done to someone who is grieving, I think, is to have someone else tell them that they’re not doing it “right.” Usually the person admonishing the grieving person is really having their own issues.
I was treated like crap by at least one friend after my dad died. She desperately wanted to supress my grieving, because it made her uncomfortable. (She even went so far as to tell me that my dad was a grumpy old goat so I shouldn’t miss him that much.) She had her own unresolved issues that would take too long to go into here, but I realized later that her treatment of me had little to do with how I behaved, it was all about her. She was freaked out, and I was a reminder to her of unpleasant things. She wanted to get me to “snap out of it” so she wouldn’t have to be reminded that we all have to confront loss and grief.
I’m just telling you, you might encounter a few people who do this to you. Don’t let them get to you. It’s not about you at all. However you want to feel, however you want to grieve, it’s fine. You obviously loved your brother very much and it’s going to take a while to feel some semblance of normalcy. Take your time.