Hi and Welcome to Just Answer,
Ok, let's take a look at this;
It sounds like to me that your drain from the disposal to the other sink drain may be clogged...
You can test this, by removing the drain line from the sink tie in, Make sure you have a bucket to catch the water.
If no water comes out you will need to see if you can clean your disposal
If you need more help Let me know
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If there is anything else let me know, If not click accept. Thank You Michael L.