When I turn on my garbage disposal the other sink has water coming up

The same thing happened to us! We finally just got a plunger & plunged the disposal side. That did the trick! Then you can put whatever you want to freshen it up. I like to put lemon or orange peels down the disposal for a clean fresh smell. Good luck!

Might need to check your pipes there might be a clog just unscrew the pipe under your sink make sure you have a bucket under it to drain the pipes

Put baking soda + vinegar down first, run the disposal, then a squirt of dish soap followed by boiling water

You likely have a Y-joint in the PVC Or Plumbing. Either

A. The Y should have been deeper before the two consolidate to one pipe,

B. The base of the Y that connects to sewage or septic is not a diameter double of the two incoming, but was cheaply done

Both of these issues are individually capable onsetting that when both drains are in use, you get a back up in one or the other.

So, the best way to resolve this is to use a larger PVC in the base that coonects to sewage or septic.

It is a job and a bother to DIY.

You need PVC and a T-Joint or a Y-Joint and PVC Epoxy.

I would call a Real plumber to do it right this time, [or pay a friend with experience enough to not identically result same problem as you have already].

Problem is most likely due to B but is also possibly due to A, but either problem solves the same anyway:

you need more path [pipe diameter] for flow to the septic to not become obstructed

Same would occur if you connect two flexi straws to straw#3 and two mouths:

Both trying to blow bubbles in the choch-ee-moo, does not result more bubbles but instead onsets that there is force or blowback in both straws which opposes blow to resist full capacity of blowing bubbles in the drink. However if you have both straws in a Doubly large Milkshake Straw, or seperately going into the drink, you do not get same resistance and both persons can happily blow as many bubbles into the choch-ee-moo as they like.

Scientifically, it is all about 'Path of Least Resistance' that applies to anything with flow, not solely Electric Current, but plumbing, selecting a line at a store, people exitting a stadium, tramplings by a bull at a rodeo or the running of the bulls in spain, flow of milk from the carton to the cereal bowl, etc etc And Time too.

The bigger the Path, the lesser the resistance to flow.

Big stems need more water, little stems need less water.

Thus your problem causes by?

A path too small for the flow to be without resistance.

This 'path' is inside your pipes and has a distance from the pipes beneath your sink to the sewer or septic tank.