If Onii-san was a more important character, I think we would go into why he feels so socially awkward. I mean, most of it is probably because Onee-san is an attractive girl of his age, and he doesn't have any experiences with girls at all - but it feels... deeper than that if he feels that he can't even go into a Starbuckspacks without a panic attack.
But he isn't an important character, he's at best a side character, and I guess his character will always remain socially awkward.