Hi,
I had this problem. I was benching heavy ages ago and my shoulder went. I kept getting dull pains when I did heavy bench or press behind the neck.
I ended up having physio, ultrasound for weeks and eased off onto dumbells for less weight where it hurt.
Luckily the pain totally went and I was able to go back to heavy flat benches but I learned the following:
Don't do wide grip benches, slightly wider than shoulder width puts less strain on your shoulders
Don't do press behind the neck, it will do you shoulders in if you have had shoulder pain
Also follow the advice of thelion2005 - it's similiar to what an experienced guy told me during my rehab.