Hi mayorcesar and welcome to the family!

It's understandable that you have a hard time trusting your girlfriend when she keeps lying about who she is in contact with and you already experienced her cheating on somebody else. Especially with the long distance situation and after all the support you offered this insecurity must be so hard to bear.
I have some questions for clarification if you don't mind.
What happened with her pregnancy? Did she have the child?
Is your relocation temporary or for the long term?
she explains to me how she wouldn't be able to be in a monogamous relationship and how it's really challenging for her.
This is something my BPD boyfriend is struggeling with as well. There are people who decide that monogamy isn't for them and that they would rather live in an open relationship. In the end this is a question of compatibility and relationship goals. If both partners have different views on that, it's nearly impossible to compromise without one person beeing uncomfortable and having to put back their needs.
With BPD it's possible that there are other underlying reasons for this behavior, maybe a need for validation or to keep people close. But i feel those issues are equally hard to resolve and require a lot of honest communication and introspection.
Did you talk to your girlfriend about why she feels the need to cheat?
Does she lie to you about other things as well?