My girlfriend had chicken pox years ago, now i have it, is she completely immune to the virus?

Yes: From the standpoint of getting chicken pox, yes. Once you have it, it's never gone. It sits dormant near where the nerves come out of your spinal cord, and sometimes it reactivates. When this happens, it's called shingles. Someone who had chicken pox is at risk for shingles for the rest of their lives.

Probably: Immunity to chickenpox is usually lifelong but it is not unheard of to get the disease twice.