I would suggest you take a week off from all excersises that bothers the elbows.
Treat it with ibuprofen gel for a couple of days, 5-6 days.
Then get back into training, but do some adjustments to your training.
You seem to be into powerlifting type of training, so I suggest you drop all direct biceps and triceps work, except 2 sets each week for biceps and 2-3 lighter sets of French Press or similar but with a moderate weight.
Then stick with the heavy benchpress work, such as regular benchpress, board work, chains and close grip.
For shoulders, do perhaps one set of presses, then do 2-3 sets of side raises, bent over raises, rotator cuff, mix it up a little. Do 3 sets for shoulders each week, and none for the front delts, those get hit plenty with benchpressing.
That should really fix your problem.
I would be very surprised if you had a problem if you followed my suggestion. It's just a matter of downsizing the trauma that your elbow is getting.
One more thing: Keep your thump on the same side as the rest of the fingers when you squat. You will find that this relieve a lot of the pressure the elbow gets when squatting.
Good luck