A plunger may work, but it may also make the problem worse. Draino willl take days and Gallons because the starch in potato peeles gives it a resiliance. The best way to fix this problem is to empty the trap. The trap is the U shaped part of the drian pipe under the sink. Yes, you can handle this. Take a large adjustable pliers and loosen the slip nuts holding the trap on. Be sure to put a busket under the trap first to catch the water being held in the trap. When the nuts are loosened liggle the trap loose, remove and clean it out. Look down the drain in the sink, it should be clear of debris and you should be able to see clearly into the bucket. If this is also clogged I suggest using a wire hanger. Stick one end down the drain and turn it until all the waste is clear. Now that everything is clean, put the drain trap back on. be sure not to tighten these nuts to hard. They may even be made of plastic so be careful. After the trap is on, run some water and check for leaks. If you are still clogged, the peeles made there way past the trap. Now try liquid plumber or draino.. If this does not work try to find someone that knows about plumbing.. If this fails call a plumber and get out the check book.. Good Luck