When I was a kid my mother used to tell us,"Eat the rice, it will stick to your ribs". Well I don't no for certain that it will stick to your ribs but I do know from first hand experience it will stick to your pipes.
Rice and Pasta are two products that will raise shear havoc with a disposal. Often the rice or bits of pasta settle in the trap and continue to expand. In the process the high starch content then works as a glue to stick it all into a formidable mess. Believe me, no one likes sticky rice or pasta, especially your plumbing pipes.
You may have a limited success by plunging the opposite sink while running the disposal but in all probability you will need to dissassemble the trap and physically clean both the trap and the cross tubes. Pay particular attention to the Tee in the line. Both the end waste and center waste kits have a baffled tee and you will probably find the majority of the clog in the baffled section of that tee.