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.
You want to get outside into the courtyard. I'm not sure exactly where you are, but if you are where I think you are, you should come across a hallway before going upstairs. You should find an exit there that leads you directly to the courtyard, avoiding the need to go upstairs.
Once outside, you need to get to the garden (just follow the wall of the courtyard: watch out for guards) and the solarium.
Once inside, you'll hear Rulindil talking to his subordinate. Once he leaves, head to the room to the right of where Rulindil enters (again, watch out for guards). Here, ransack the room and look for dossiers found inside of a chest. You'll also find a interrogation chamber key.
Once you have that, you need to escape. To do that, head down into the dungeon, once more dealing with the guards that you find there. You'll find a prisoner locked up as well as a chest that contains another dossier.
Finally, you'll need to speak to and release the prisoner: Etienne Rarnis. Once freed, you'll be rushed by even more guards. They'll have the trap door key, which you can then use to escape the embassy directly from the dungeons.
When you drop through the trap door, you'll enter a cave where you'll have to fight a troll.
After that, you're home free.
Best Answer
Those words just depend on your race. If you're a High Elf, go out the door to the guard and tell him Elewen needs him. But I know you aren't a High Elf because of the way the Thalmor soldiers say it.
Here are the dialogues of Thalmor depending on race.
High Elf: Must be new around here.
Wood Elf: Seems a bit short to me.
Human/Dark Elf/Orc: You there. I don't think I've seen you around before." or "Come here. Let me see your face." or "Haven't seen him/her around before." or "Must be new around here [This must be one of the races you're using].
Beast [Khajiit or Argonian]: Wait, is that a tail?
If you're an Altmer, you can tell the Wizard at the door to talk to Elenwen. You must use Speech. If you fail, the courtyard will be hostile.
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