Sometimes I just feel like I should be giving up.
why do you want to give up?
My girlfriend is too insecure. she always worries  about my past.
You should talk to your gf about it and assure her about the relationship. If you really love her dont give up that easily.
I love her but I'm not sure what to do. She won't believe that I've changed and I don't have time for her insecurity.
If you really want her, then you need to work for it. Relationships worth having can't always be easy, and sometimes require a lot of trial and error as well as plenty of serious conversations.