I'll move the topic to Women's Issues, since he clearly wants female responses primarily.
As for my opinion: Your girlfriend needs to open her eyes. Many people masturbate while in relationships. She shouldn't get jealous. As someone else said, it's a heck of a lot better for you to masturbate than to say, cheat on your girlfriend! Why don't you tell her that? She might not like to hear it, but then again she may be at an age where she still needs to develop some maturity and understanding.
Heck yeah it's normal. I masturbated even when I was dating someone for two years and engaged to him!! I still touched my'self when I was alone

Masturbation is a very personal thing, and it is not "self-sex" in any sense. It is different emotionally and physically from real sex.