Alright, this thread is a picture dump so I'm just going to scan for the OP's posts.
You didn't provide a huge amount of information about this, but it doesn't sound too different from what I went through a while back. It's always easy to just say, "If she's just going to listen to your parents, she's not worth your time," but the fact is a lot of those feelings and possibly fears are buried deep down in habit, and doesn't necessarily mean that your girlfriend is prioritizing their word over yours. It just means that your relationship is built on a really dangerous fault line and you're both going to have to work extra hard to get things to work out.
As someone who is polyamorous, it's kind of hard for me to give recommendations as to what you could do about your parents pushing her to date another guy. Ideally I would say that you two should be able to share her, but given that most of the world doesn't work like that, such a suggestion may not be entirely realistic.
Right now my biggest suggestion is to make sure that you and your girlfriend are communicating with each other. That was the biggest source of pain between my friend and me; we didn't have a long talk about it until a year and a half later, and we both regret that. Make sure that you each know what the other wants, and try and work together to formulate some kind of solution, even if it's not perfect.
If the two of you can talk openly, then it should really just boil down to how the two of you feel toward each other. And then all you can do is follow those feelings.