Can you file a lawsuit on a prison if you're severely hurt?

If you were an inmate, then you knew what kinds of people you were incarcerated with. Just what do you think the prison could have done? Don't you think that you had more control over the situation? If you had not committed the crime, you would not have gone to prison. If you had not gone to prison, you would not have gotten a broken jaw. I am not trying to be funny, but just how is a prison supposed to deal with all of those bad guys? Society puts them into a secure place so that they don't commit crimes, but since they are bad guys, they do bad stuff no matter where they are.

You can, but you will have to prove the prison was negligent.

Possibly, but you would have to show the prison was at fault in that they violated some mandatory law or rule and that that violation directly resulted in you getting hurt.

Generally the prison is not liable for intervening criminal acts of other inmates. Your only potential cause of action would be if they negligently supervised to the point that their neglect was part of the causation of your injury. What you are seeking to bring is a very very difficult case.

Yes, it's done all the time. Such suits rarely succeed.