Oh, that sounds very painful and I'm so sorry you're going through so much. Having screws put in, I agree with you, they should have put you in some sort of physical therapy to try and easy your knee back into normal movement. I'm very surprised they didn't honestly.
If he's going to have the screws removed now however, has he told you what else he's going to do or does he just expect your knee to heal properly without them? Has he spoken to you about knee replacement surgery at all? I know it's just a break in the Patella but if split the entire bone the whole way, that can be a very difficult recovery and it's hard for those types of bones to heal properly when broken like you described.
I would speak with your doctor again about the pain and see what he plans on doing about it, especially if he's trying to avoid the physical therapy. If he doesn't give you a satisfying answer, I would look to consult a different doctor all together. I found some information about knee implants that you might want to discuss with your doctor. It's information for both a total knee replacement surgery and just a partial knee replacement. Basically the implants themselves, the manufactures of the implants and what all goes into the surgery itself. It even discusses some of the top implants that are used and why they're the better choice. I hope you don't need to go this route but it's something to think about.
I wish you all the best!!http://www.healthline.com/health/total-knee-replacement-surgery/implant-manufacturers