I broke my shoulder just before Christmas. I broke the humerus completely where it meets the humeral head and fractured the head as well. I also had pain like you describe, as well as a lot of pain around the elbow.
Have you got the type of sling that covers the lower arm or the one that just fits round the wrist?
I also had awful bruising that took the best part of 5-6 weeks to go.
Are you sleeping in the sling? I was told I had to but by about 3 weeks post break I found that keeping my arm in that right angle position absolute agony. I would wake up crying because it was so stiff.
I used to lengthen the strap at night so I could straighten my arm while in bed.
I was told at my 3 week appt to start gentle excercises, just letting the arm hang and moving it back and forward slightly.
This I did as much as I could and it really helped, especially as due to Christmas I couldn't start physio until 6 weeks post break.
One thing that really helped was my grandson's beanbag especially in bed. it moulds to shape and I found it very comfortable.
Do take painkillers if you need them and contact your fracture clinic if you are at all worried.