I just told my girlfriend I cheated on her
Why did you tell her that?
Because I felt guilty
I'm sure it was hard for you to do that and I respect you for being so honest about it.  Not admitting to an infidelity and having it be found out later can destroy a relationship.  I'm sure this was for the best!
I actually do feel a little better. Maybe I should just lie about something else instead.
Well I don't think you should lie to her at this point. It sounds like you guys should just break up now and move on.