Dating sites are like the bars used to be. I would guess that literally TONS of guys send messages to the same girls you are writing to. Maybe you shouldn't look at those sites as a primary source of dating opportunities, but rather, yet another venue that should be used in addition to traditional ones. Also, keep in mind that dating is a numbers game: if you ask enough girls out, one will eventually say yes. You just need to develop thicker skin so as to handle the rejections more appropriately.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?