when you said that it hurts even in your warm ups sets, i thought wow that could be quiet serious. but then you said it doesnt hurt when you do behind the neck press and dips, those are two exercise which people offen find hard on there shoulders, but it doesnt hurt you, so i am confused and have no idea, maybe one of the more experienced and more knowledgeable guys would help you out.
but i do have some advice for you, stop doing the behind the neck presses. i used to do them too and after talking to the people on this site i got told to stop doing them. they are really bad for the shoulders, and most of the people on this site, know exactly what they are talking about, so i trusted them and just did them to the front. just do normally shoulder press, your shoulders will thank you in the long run.