Yes, exits are relative to the direction you enter from.
Have you exhausted all possibilities? Remember the top and bottom of the map wrap round. You could also return to the entrances on the left and explore s other path. Rooms can also be searched, with a 1 in 4 chance of finding a secret door. Teleport Traps and backslide spells can also move you to undiscovered squares.
However, if all those avenues have been exhausted, I guess it is a loss, unless you have any other characters with backside, or a grappling hook if the way has been blocked by a chasm etc. I have never had a game which ended in dead ends, but I guess it is still a small possibility despite the ways around mentioned above!