The wrist wraps might help some, but I don't necessarily think they are the ultimate fix. I would suggest looking at your overall program and make sure everything is in balance and you aren't overdoing one area at the expense of another. I would also recommend shoulder stretches daily. I had chronic shoulder soreness, tightness, and kept injuring my pec. It was mostly related to my left shoulder being very tight which caused me to line up under the bar off center for squats and kept it hurting all the time.
At your age and strength level you shouldn't have any problems because of years of heavy training, which makes me think you have some tightness or imbalance somewhere which is the root cause of your problems.
Here are some things to examine and consider:
1) Ice your shoulders and elbows after every lifting session no matter what you did
2) Work on shoulder flexibility
3) Warm up your shoulders and upper body with some arm swings and stretches before every session, even when you are squatting
4) Stretch your pecs, shoulders, and lats every day
5) Consider getting some indian clubs or making something similar and using them to improve your shoulder mobility
6) Make sure the bar isn't sliding during your SQ sets. You may start out OK, but if the bar slides down during the set you may end up supporting the weight with your arms
I know this sounds like alot of things to do/consider, but almost every older lifter will tell you they wish they would have paid more attention to warming-up and working on flexibility and mobility when they were younger (before the aches and pains and injuries really caught up with them).
