Pain with pullovers
 

When I do pullovers I feel a pain in my shoulder. It is more of a strain. Would it help if I changed my grip on the bar?

Grip: possibly.

Are you going really heavy, and too soon?
You could also be pushing your ROM beyond what your shoulders are comfortable with.

My thoughts. Have you tried with a DB? The bar may be putting your arm in a compromising position. Would be helpful to see you doing one before trying to diagnose.

I say that you could try it with a different grip. But also look into what bamazav said, maybe you could post a video of you doing it to get the best answer.

Remember the RICE rule!

R est for a while
I ce to help soothe the pain
C ompress the injured area with a bandage
E levate the sore area

Are u loosening up your shoulders and rotator cuff properly before your workout?