If you are on a shelf at lava level, you are best off going up that cliff, getting to a higher ground. Build a tube out of cobble with ladder inside, hugging face of the cliff. You will likely emerge on a higher plateau, from where you can explore easier. At this time, it might be a good idea to break your existing portal and rebuild it at a more convenient location. I generally find most traversable landmass in the nether is in the Y=60-80 range.
Building a tube out to the ceiling is also an option. But once there, I would rather suggest building a horizontal tube just under the ceiling. You can build sides against the ceiling, and then build out the floor, without exposing yourself much. I do not advise digging in the ceiling itself cause while safe, it really gives you no idea where you are. Tunneling at Y=120 is good when building the fast transport network and already knowing the coordinates.where you want your portals. Not when you are still exploring/looking for fortress.
You can also build shaft/ bridge using pistons without exposing yourself to ghast fire. A piston pushing blocks will 'squeeze out' any lava. So if piston will not extend when activated, it means it got 12 solid blocks in front of it. This technique can even be used to punch your way through a lava ocean in the event your portal generated in a cave under lava.
If you are not averse to cheesing it a bit, you can start a creative world with same seed, and then just fly around the nether a bit to see where things are.
If you post your world seed, and your portal coords, some here can offer a bit of more specific advice.