My name is Ben and I'm a posture Alignment Therapist and Personal Trainer. I've had the same issue you have had about 5 years ago before I learned the ins and outs of correcting postural position. Bellow I will discuss briefly why you are having this problem and what cues you should look at, pertaining to your own body, that is causing this issue...
Shoulder issues are generally a direct result of shoulder position. In your case, it was more than likely improper shoulder position while lifting, causing to over use of your shoulders as oppose to your chest and back (the prime movers for these push and pull exercises).
Often times people that have a rounded shoulder position due to dysfunctional posture have a difficult time attaining a neutral shoulder position. What needs to happen before you lift is corrective exercises that address this shoulder position, often times also addressing other related postural issues such as kyphosis (thoracic rounding) and lardosis (excessive curve of the lumbar spine), as well as other postural dysfunctions that may be leading the improper loading of your shoulders during these movements. Everything is connected and related, so you must look at your overall postural position.
The first step would be to look at yourself in the mirror and analyze where the imbalances are in your structure. Are your shoulders rounded? Do you have forward head position? Is one of your shoulders higher than the other? Is one of your shoulders rotated more forward than the other? Do you have an elevated hip? Do you have one hip that is rotated forward? Do you have an anterior pelvic tilt or a posterior pelvic tilt? Are your feet everted or inverted as oppose to neutral? There are other aspects to look at, but these will keep you busy in thought and research for now in how to address these dysfunctions leading to the compensation that caused your injury.
The key is to bring your body back into balance to attain a more ideal postural position. Once this occurs, your body will start to find proper function within movement in whichever exercise you are doing. As a positive consequence to addressing your overall posture, your shoulder should be able to heal faster because you will no longer be over using the wrong muscles through compensatory patterns.
I know I threw allot at you, so don't hesitate to ask further questions...