I put to much food down my garbage disposal and now but sides of the double sink are backed up. ?

I tried using a plunger first on both sides of the sink but that didnt work. I then bought some liquid plumber gel and it didnt work either. It clooged up when I was trying to dispose of some beef stew with potatoes and meat and carrots. I know that the pipe goes striaght from the diposal to the sewer or whaterever. Are there any natural remedies or maybe some acidic stuff that will eat up the food so I can use my sink and not call a plumber?