Why won't my kitchen sink drain? Disposal is working but when I run it water backs up into single sink
There is (obviously) a blockage.  First off, watermelon rind should not be placed in a disposer, it's too tough and fibrous and often clogs up the drains.

If you took apart the P trap and found nothing, it's either blocked before or after the trap.  Most likely before, at the outlet of the disposer.

Take all the pipes apart and find the blockage.  If there is nothing there, then it's in the drain past the part that can be seen below the sink and you need either better tools, like a longer snake or you need to get a plumber in who can clear it for you.