Yvette,
My guess is that the two sinks share one waste trap under the counter. Open the doors, and look under the counter. Do the two lines from the two sinks come together and go through one "S" shaped trap ? If so, that's probably where your clog is, and the best way to clear up your clog without chemicals will be to remove the trap. If you want to try to do this, post back and one of us will guide you.
BobB