Is it normal my boyfriend is obsessed with himself?

The truth is this is not uncommon anymore. This generation you have lots of guys that take selfies, look after themselves and their appearance. I've noticed it to be more common in younger guys, but it exists in older ones too... maybe to a milder degree. I think I would call it metrosexual not necessarily narcissistic... that'd be jumping the gun a tad

I honestly don't think vanity is that big of a deal as long as he loves you. But vanity in a guy can lead to other things too so it's a judgment call