Welcome sky367: Sorry you dealing with a breakup. They can be very painful and hard to deal with, especially when it wasn't your idea to breakup.
She keeps saying that I'm obsessed and that shes annoyed and thinks I'm "following her". I would love to remain friends with her but I don't know how to further a conversation or try to have a friendship with her.
You probably want to be careful, as you wouldn't want to be labeled as a stalker or have her get a restraining order against you. Give her some time and believe what she says. If she indicated she wants time to work on her mental health issues, you have to respect that. Let some time pass. The more you try to force the issue, the more she won't want a friendship.