Your injuries put those scholarships in jeopardy–even your father should realize that. Yes, you will have to grow a pair and stand up to the coach and your father. If you have been complaining about your arm for a long time, yet are still going to the mound and getting good results, these individuals may feel justified in ignoring what they consider to be your constant wolf cry.
If you need the surgery, you will need to find a way to get the surgery, even if it means stepping on some toes or reporting whomever you need to report. It’s your arm, it’s your scholarship, it’s your call. At a minimum you can shut yourself down and decide not to throw until you get that surgery and recuperate.
You will need to find a way to get the support you need from the people around you. What does your mother say? Perhaps she’s the way to get through to your father.
I’m not a counselor, and I understand it’s difficult to speak to people in authority. I had to recently take control of a situation surrounding my son’s pitching. His arm has recovered because I stepped in and prevented his over-use and abuse.