First, check the humidity level in the room where the piece is located - easily done with a hygrometer which you find on many weather stations and cheap digital thermometers these days. Or buy a traditional one for around £25 upwards and enjoy it alngside your antique.
If the room has a very high relative humidity you will be damaging the antique if you keep it there. Glues (which used to be water based) can become weakened, veneers will wrinkle and lift, boards warp, joints open, mould grows etc etc. The sticking drawer is a warning. This is why museums and historic houses all have hygrometers in the rooms - to protect the contents.
Because wood is a living material it will always swell in damp surroundings. Best action is to keep your expensive antiques in a dryer environment (this goes for silver and paintings too!) If you insist on keeping your antique in a very damp environment the only option is to sand down the sides of the drawers to allow it to fit. Best ask a professional restorer to do this if it's a valauble piece.
In general, always use natural products and materials where possible. Natural waxes and French Polish - NEVER silicone or varnish. Try to find a local supplier of natural products via google or similar.
Mr Big, January 2007