no, don't force through the pain...pain is there for a reason. its a WARNING.
I'm a PT and I can tell you when there's inflammation, there's swelling filling up a space that would otherwise have free space to move. This is where "impingement" and such diagnoses come from...
Continue exercising but do this:
1. Choose exercises that are below shoulder level..this will allow you to use your shoulder with the maximum amount of joint space available..You don't want to move in a position that causes repeated bone on tendon contact.
2. exercises that allow you to keep the upper part of your arm fixed or supported will help
3. Ice for atleast 20 minutes after exercise. Medical books will say it takes 20 minutes to penetrate deep enough to do any good. If you're a big thick muscular guy, I'm envisioning a shoulder like a bull's which would require longer for any benefit.
4. every day life: posture is actually more important than you think. If you're slumped over, it changes the position of rest for your shoulder joint. sitting or standing tall/upright will help with the posture and this will help not aggravate your existing condition.