(If you spawned in the Nether something would seem to be wrong.)
The lava sea level is Y=31 so I would suggest digging sideways at around Y=40, sooner or later you must come out into the open, though you might have to go back to the Overworld for more pickaxes (or craft some more where you are).
If you want to try again with a new portal you need to build the new portal in the Overworld at least 1024 blocks away from the first.
(Or break the portal in the Nether and kill yourself to get back to the Overworld.)
Once you are out in the open you can build a portal there and build a new one in the Overworld with its X and Z coordinates approximately 8X the X and Z coordinates of the portal in the Nether.