@shackleford OK, good information. I was intending the front squat to be a diagnostic tool here - but if you want to incorporate them into your training, great.
You should do the band and wall stretches mentioned. With the difficulty keeping your elbows up and your symptoms with the back squat, try to first unload your elbows some with training, ie, if you're doing a lot of curls (a huge stressor being barbell curls) those will really strain the tendons of your elbow joint. You want to especially stretch the musculature surrounding the elbow joint including your forearm/wrist, triceps also, and unload the elbow joint itself. For curls, either take a break, or do hammer variations or turn your grip sideways for them. Doing skull crushers kills the elbow and the flexibility around the joint, so drop them for a while. I believe if you do these things for a short while you should get some feeling back in your arms on the back squat. The ulnar nerve may be a bit compressed.