Using xbox, I cant get out of water chamber in the Hidden City area. I can climb wall and swing to platform but to then exit cant get out of area.

By water chamber, do you mean one of the tombs?

Yes after swimming through tunnels you reach a tomb where you climb a wall then swing to a ledge and inter a chamber with a coffin Then there is no way out.. 

If it is the aqueduct tomb that gives the Jaguar Paw skill, the way out should be either a zipline to the edge of coffin area that leads to way out. If my memory is correct.

If not, may be just a simple backtracking to get out of tomb.  Alot of the way out of tombs are back tracked a ways from the direction you came from going to the sarcophagus

What Big T said. ^^ If you're still unable to find the way, seeing a screencap of where you are on the map and what it looks like in the game can help us help you.

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Got it, had to return the way I came but it kept trying to turn me around, Had to force the turn back. Thanks ( back in the water)

 

Glad you were able to figure it out/ leave the completed tomb