Yes, I’ve had two differnent kinds of elbow pain from low bar Squatting as well as some shoulder pain. A lot of it is due to a lack of flexibility in the shoulders.
The most common pain I’ve had is at the medial epicondyle, where the flexor tendons insert. I get this pain if my shoulders are tight, and I pull my elbows under the bar. I always try to pull my elbows forward because it keeps me in a more upright position, but if they are killing me, then I don’t pull them as far forward, but make sure I squeeze my scaps together even more than normal. I’ve found that massaging the affected area helps, and I ice my elbows after every session regardless of pain. Advil will be your friend as well.
The other pain that I got was a sharp pinching pain, and then some pretty decent inflammation in just on elbow. I think I got the bar a little low, and should have reset before starting to Squat, but I did the set regardless. For the next few weeks I had to switch back to high bar on the lighter sets, and then just bear the pain on the heavier sets. I iced 3-4 times per day until this was resolved, and mega dosed the anti-inflammatories as well.
In a nutshell, I think a lot of it stems from flexibility issues, and much of it from the shoulders. However, I’m sure working on stretching the wrist flexors would be beneficial as well.