That's really good progress. I think many cats crave human interaction and contact but they have trust issues to let you pet them. Just let her keep coming to you and pretty soon she will be greeting you at the door.Well she let me pet her last night. I just laid on the floor and hend my hand out and she eventually started getting closer and gradually let me pet her and then got really cuddly and was walking in circles and rolling on the floor. She pretty much stayed under the bed still but came out from under it a few times and then went back. She’s a really sweet kitty.
re: vet - unless it is urgent, let it wait.