It certainly sounds like nerve compression. And it could certainly be TOS, or it could just be at the elbow. The showing up at the same time could just be chance. It's not like bilateral TOS sides are required to take turns.

Are you sleeping on your stomach? This is generally considered bad. A little web searching will provide details.

Are you sleeping with your arms above your head? Also bad for the nerves.

Other than that, see what the Dr. says. Also see if you can find a good PT or chiro to evaluate your posture, alignment, muscle tension and various suspect body parts like neck, shoulders, back, chest, etc. Early in my journey these folks were pointing things out about me that I hadn't been aware of.

Good luck.