So I currently have mononucleosis.

I was wondering about after people heal.

Do they gain an immunity?

Can kiss my girl friend if she has already had it in the past?

Mononucleosis -- familydoctor.org

Mononucleosis

Once you have mononucleosis caused by EBV virus, you always will have the virus. Your body develops some immunity that usually prevents severe disease again. You may have recurrent mono throughout life. However the infections aren't as severe as the first time. EBV virus is associated with neoplastic disease later in life. It is the cause of Burkit's Lymphoma, and can cause other types of lymphoma.
So, if your girlfriend previously had mono, and you have it now. It is more likely that you got it from her in the first place. So, you won't give it to her because she already has it. You can kiss all you want because both of you now have it.