Side sleeper here, i have very firm mattress. Shoulder pain is probably not because of the mattress, but because of weak muscles. Training your upper back/shoulder muscles just a bit will help a lot. I had a shoulder injury (bar/pub accident, yup.) which caused me to avoid using certain muscles. Got pain in my shoulder as well. Fysiotherapist recommended some excercises and it disappeared.

I have a firm mattress because i had a sore back, which in turn caused me to wake up tired.

A sitting non physical profession is the cause of all this. Sometimes i do have a sore back, but going to the (climbing) gym fixes it for weeks.