Can Muscle Compensation Be a Long-term Effect of Botox?

One thing is possible regarding your situation. Sometimes, people don't notice things about themselves until they actually get something done. This is a common thing that happens. When you get something done, like Botox, you tend to look at certain parts of your face more closely and notice things that used to be there before. That is why doctors have become used to pointing things out to people so that this doesn't happen after the particular procedure.
We are asymmetric for many reasons. One thing is really interesting though. When people look at others to asses beauty we tend to look at the right side of the person's face predominately. This is due to the fact that our right brains appreciate beauty more than the left brain. Our visual fields are crossed and asymmetric which leads to this phenomenon. You can find this out by searching on the web for visual field pathways in the brain. Hence, we select one another, from a sexual selection stand point, by concentrating more on the right side of the face.
In terms of the possibility that other facial muscles are working harder to compensate and then subsequently leading to asymmetric muscle movement and size differences, This is a possibility that hasn't been looked into as much from a scientific standpoint and could be happening. I would have to see pictures myself to really come to some assesment of the situation. Botox could help in this regard too. You could put Botox in those muscles that you think are bigger in a very conservative way. I would talk to your doctor or send me pictures.
I hope that helps!

These symptoms are unusual from Botox stand point and the underlying issue could be other medical conditions.  It appears that you are being followed up closely and are undergoing testing for this condition.