I'm 28 years old with a 21 year old girlfriend....is this wrong?

I am 28 years old with a 21 year old girl who wants to be my girlfriend...problem is we have only known each other for 10 days, but we have gotten to know each other so well over the time we have spent with each other...But there are a few issues I have that are bugging me...1. the age...I feel like I am in the wrong morally for dating a 21 year old...2. we don't exactly share the same interests in music...She really likes bands like Korn, SlipKnot, etc...the only thing we have in common is that we both like She Wants Revenge. 3. My current situation in life...I was in the hospital getting treatment for depression(I am a Army Vet and served in Afghanistan)and now I am living in a "halfway house" for Vets and I feel really out of place there...I want to get my life back in order, but I am not so sure I am willing to sacrifice my relationship with this girl to do it....I am torn up inside emotionally...can someone please offer me some advice or help me out?