Last night I think I put too much in the garbage disposal when the dishwasher was running. Water backed up in to the sinks (dual kitchen). When the dishwasher was finished I took off the trap under the sink cleaned it out then cleaned out the outlet going to the main drain in to the wall and then ran water with a bucket underneath the drain and turned on the garbage disposal. Nothing backed up so I assumed it was not the garbage disposal. But when I put it back together the drain backed up again. So where's the clog? The hose going to the dishwasher or the outlet going in to the wall?
Since you cleaned the trap and the outlet to the main, the only thing left is the main drain going to the sewer line. You can try to use a plunger on the main bowl. You will need to cover up the other bowl drain with a piece of rubber, unless it is also full of water. If that fails then purchase a hand held auger and run it down the main drain once you remove the trap and inlet pipe. They are not that expensive and you will probably use it many times again.