Is it possible to trap yourself in the Nether?

According to the Wiki, you can find both Obsidian and Flint and Steel in Nether Fortress chests. Go find a nether fortress and try your luck by collecting chest loot.

I see multiple ways for you, to get back with minimal losses.

1. Like Quijibo mentioned, you might get lucky by finding obsidian in Nether fortresses.
2. Since the nether is unloaded when there is no player in it (in general of course there are ways to have it loaded), you could drop all your items near the original position of your netherportal, jump into the nearest pool of lava, respawn in the overworld and reenter the nether through the overworld, which should generate a new portal and your items would still be there. (Or get a chest from a fortress, in that case you don't risk any despawn)

In Minecraft 1.16, you can find nether gold ore and craft ingots by making a crafting table (you can find wood in warped and crimson forests) then craft gold ingots and barter with piglins until one gives you obsidian.