Should I use a plunger? If so, I will have to go get a sink plunger.
But I am wondering whether the plunger might damage the disposable's
grinding unit which I think is congested right now I'll go try
getting
more rice out.

Something you don't probably know, but I'll tell you ..............

I didn't know it for a long time, but once I found out this secret, it
helped me infinitely with disposal clogs ...................

That silver tower that is about as round as a silver dollar and three inches
tall there on your sink ............

that's the vent for your garbage disposal and, I think, your dishwasher.

If your sink has one of these, in order to plunge your disposal, you will
need to seal that up. First, pull the silver cover off. It comes right
off. Next, put a VERY wet rag over the top as much as you can cover and as
best as you can cover. This will stop the air from going in and out of that
vent as you plunge up and down. Sometimes, this requires three hands, one
to hold the rag, one for the plunger, and one to hold a plug in the adjacent
sink. Or you can put the plug in and fill the sink. A helper to hold the
plug in there helps.

You can feel when you blow the clog, the plunging gets easier.

Plugging the air vent and plugging the hole in the adjacent sink will
shorten the amount of time you have to plunge, and it plugs up the air route
so you are pushing on water instead of having a hole where air can escape.

Otherwise, you can really work up a sweat, learn new cuss words, and never
have any noticeable effect on the clog.

HTH

Steve