You have gotten a lot of garbage advise except from Otter.
I know of a similar situation with a freshman. Most talented runner in the team in years. Training was not going well. Set some records early on but results began going downhill. Athlete blamed training philosophy. Went to a different sport. Did great and had the numbers to get recruited but decided against it. Went to top academic U. Just tried out for track and made the team - avg D1.
I have met both coach and athlete above. Athlete was independent (a little nutty) but very talented and a top student. Coach was headstrong and reportedly having a panic attack during that particular incident. Reports are that coach later regretted the incident. Coach was not liked by anyone in the team and that negativity may have contributed to the freshman's decision. Met the coach and found nothing wrong with him. Really clueless about all the negativity. Others on the team blamed those who were not into running but looking for an EC. Coach apparently reads a lot about running but just doesn't get it. Lots of injuries on the team (real or fake, couldn't tell you).
I would say that such situations are unfortunate, nothing else. Think about shaving off a little ego. Expect a little more from a coach, an adult. No, I do not agree with your coach to make you run when injured. You do not owe further injury to anyone for any reason.
Public HS grounds are public. But you can't stop a football game just because you want to stretch in the middle of the field. The rest of the public also has rights and your right should not trump theirs.
You chose a different path. Good for you. Stick with it. Train yourself as best you can. When you think your training is showing results, show up, watch the practice from the stands - that's allowed. When practice ends take the field and put on an exhibition. A mature coach, will find a way to make amends. If he can't then you are better off staying away. But realize he does not have to beg you. You and the coach do not have to be friends and neither of you owes anything to the other. It's a student-teacher relationship. But if running is important to you, you are far better off being part of the team. So give it a try, following the path you chose.