Get a snake and pull up whatever is blocking the pipe. You can also go underneath the sink and undo the U shaped pipe area and find out what is clogging the pipe.
I always try boiling water and Dawn. It’s a great surfactant to remove sludge. https://chemistrycachet.com/coolest-things-you-can-do-with-blue-dawn/
Hi I use once a month on all our bathroom and kitchen drain to clean them.
Bi carb soda / white vinegar.
pour Bi carb of soda onto the drain part of the sink, then pour the vinegar, it will start to sizzle, leave it for 10 min or half an hr then turn your taps on and it should clear up with any luck.
Tx. I think it worked. Must do it more often.
Call a plumber... if you use a hoe you might break the pipe