Hi Boss....
Since my name popped up...
As others above mention...usually drain cleaners work short-term or not at all.
Tom covered the drain cleaning, but I wanted to drop in and mention the first thing I do when a customer tells me they have lots of hair falling out.
First thing I do is to
remove the stopper from the pop-up assembly and then clean the
stopper itself and then use a any long tool to remove and soap/scum/hair that may have built up on the sides of the pop-up assembly/drain pipe. Here, remove the
retaining nut and pull back on the
horizontal pivot rod to allow you to remove the stopper itself from inside the sink. I follow through with a hot water flush (stopper still out) and that will sometimes fix everything.
The retainer nut must be re-tightened before flushing or it will leak underneath when flushing. After the flush, remove the retaining nut again, install the stopper and insert the horizontal pivot rod into the hole in stopper and re-assemble all.
If that doesn't improve things dramatically, time to get out that snake and go fishin'....
Good luck...
MARK