Clogged plumbing in bathroom sink
I know that you said you cannot get the cleanout plug - but this is your best bet at removing large debris.

Try:


Wrap a small towel over the plug and turn counter clock wise ("Righty tighty, lefty loosy")
Use an adjustable wrench to break the cleanout plug free


If the above attempts do not work or you have already done that route:


Use a drain snake to free any debris causing the clog
You can use a toilet plunger by placing it directly above the drain in the sink, fill the sink until there is enough to create suction; (be careful not to splash too much)
Believe it or not, if a graden hose is accessible and long enough to reach the sink, place the hose in the drain and have someone turn on the water. There will be sufficient pressure to dislodge any debris.


I'm not a fan of using drain products, but if you must, go to your local hardware store and consult someone as this community covers the entire globe, it is difficult to give you an exact recommendation.