How to escape dragonsreach dungeon

You've likely hit a bug.

While you've agreed to help Sinding, it doesn't lock in your choice: if you attack him at any time before the end of the quest (when the curse is removed from the ring, allowing you to take it off), you lock in your choice to help Hircine.

However, doing so is supposed to go down differently: you act as one of the hunters and chase Hircine through the grotto, ending with you skinning him. He's not supposed to appear in jail.

You can try that: kill him in jail and skin him. If that part isn't bugged, Hircine should appear and complete the quest for you. As a reward, the ring will disappear.

Otherwise, welcome to a Bethesda game, where crippling bugs like this are par for the course in the first couple of weeks after launch.

Open the console using the tilde key (~) and type TCL (which toggles collision, letting you go through walls or other solid objects). Once you're in a safe zone repeat the process to turn it off.