Oh those sink and tub drains love to collect hair......they weave together to form a mat that can totally block the drain........
Is this a Pop-up drain? The little nut on the backside of the drain pipe is removed ........and the connecting rod is removed from the drain pipe....
From back on top in the sink the whole pop-up can now be removed........ewwwww! and along with it a long string of hair and goo...........you might also remove the P-trap and fish the hair pins and lost tweezers from in there..........
Just replace all the parts and marvel at your skills.........