I turned on my garbage disposal and the water is coming up instead of going down I previously peeled some carrots could this be the problem?

Stop the disposal and put a bucket under the trap after the disposal. Remove the trap and clean it out. Once reinstalled flush with several gallons of warm water

If Bobs solution doesn't get it then the blockage's farther on downstream. Remove the bend of the trap and send a snake up into the wall. You'll hit a bend about 8 inches in but once past that you only have 6 more feet to put out. Flush with a tub full of hot water, Good luck, Tom