Since your kitchen sink won't drain either, you may be able to clear the clog yourself. Look under the sink and you will see the drain line going down and back up like a sideways "P". That line will connect to a vertical pipe in the wall behind the sink (call it the waste drain pipe - WDP). Is there a fitting with a large square nut looking thing on the WDP just above where the line from your sink connects to it? If so, that is a clean out fitting.
If you have a cleanout fitting and want to try clearing the clog yourself, go to a hardware store and buy a 25 foot snake and a pair of rubber gloves. A 25' snake will probably cost less than $15. Lay a blue tarp on your floor to protect it from getting soiled when you pull the snake out. When the water drains somewhat, carefully unscrew the square nut to access the inside of the pipe. Feed the snake down the pipe while a helper spins the snake clockwise using the supplied handle at the free end of the snake. If your clog is within 25 feet, you can clear the clog.
If you think you cleared the clog, turn the sink faucet on VERY low flow and see if the water drains. If the clog still exists, the water will start spilling out of the clean out so have a pan there to catch the water and rags to wipe the water. If the clog is cleared, run hot water down the drain while the snake is still in the line to clean the snake. As you pull the snake out, have your helper spin the snake to help clear the sludge on the pipe walls while the hot water is running down the drain. As you pull the snake out, it should be fairly clean so just wipe it with a rag as it is being pulled out.
Keep the snake for future clogs which you will almost surely have since you have this clog. If you have problems pulling the snake back out, have your helper spin the snake counter-clockwise while you pull the snake out. Since you put harsh chemicals down your drain already, be SURE to buy some rubber gloves to wear while you're snaking your line. If the clog is more than 25' away, you could try a 50' snake (MUCH more difficult to handle) but probably call a plumber. If you're unsuccessful, you're only out a few bucks and had a lot of fun...
EDIT: Yes, do wear safety goggles like the other posters suggested.
Need more help snaking your line, ask.
HRG