A plunger often pushes a hair clog deeper into the trap. You need to pull it out, not push it down.
For less than $5 at any hardware store, you can buy a “Zip-It” tool—a long plastic stick with barbs. It’s essentially a modern, disposable version of the wire hanger, but far more effective.
If nothing else works, the clog is likely deep in the curved pipe under the sink (the P-trap). This sounds intimidating, but it’s a basic DIY task.