I have had similar pains in both my shoulders for several years. That has often been termed 'frozen shoulder'. The pain is so bad sometimes that I am in agony and cannot move my arm or shoulder at all. When it is like that, it can take a week or so to ease off. I can't sleep or doing anything much.
Earlier this year, I went to my local A&E at 6 on a Sunday morning as my right shoulder so bad I didn't know what to do. I couldn't wait for the doctor to open the following day. After various checks (injury, heart etc) they explained that it is something they termed 'Impingement Syndrome' (I had never heard of that and neither had my GP). The hospital explained that my muscles spasm and cramp and I could believe it from the pain. They gave me powerful painkillers (Codeine Phosphate) which they said I could mix with Ibuprofen and paracetamol when the pain was very bad. However, be very careful! I prefer not to bother with paracetamol as it is dangerous. It's tempting to take too much when the pain is bad and I make sure I don't.
The A&E told me the condition is just something that comes and goes occasionally and there is not much that can be done. I agreed with that as I have had spasms and cramps since childhood in all parts of my body. I have always suffered stress and it has always been put down to that. I'm 45 now and completely used to it.
I will say that I have yet to recover full movement in my shoulder from the episode this year which lasted about two weeks. I still can't lift my arm above my shoulder but the pain has gone. The GP offered physiotherapy but I didn't bother as things eventually return to normal.
Perhaps your boyfriend's condition is the same Sophie as it certainly sounds familiar. If it is, then it is something that occasionally happens and it goes after about a week. The painkillers are the best help - but please tell him to be careful with them! All the best!