One possibility is that you clench and grind your teeth more in this position due to discomfort. Your dentist can look at your teeth and tell if you grind them.
Have you tried only sleeping on 1 pillow?
My doctor advised me many years ago to only use one pillow. I found the neck pillows that you can purchase these days were very uncomfortable and didn't suit me. I have to sleep with my shoulders off the pillow too because of neck problems.
The other option is to try and sleep in a more propped up position so that you do not put pressure on your shoulder.
It appears that your head pains could be from the arthritis in your neck.
Not sure what the rheumatologist can do if you have degeneration of the bones in your neck.
Do keep out of draughts and keep your neck warm by wearing a scarf.
Visit a few radiologists. Look at the base of the skull, fluid reserve at the medulla, posterior fossa cysts. Also you may upload the images of your MRI, maybe experienced people could suggest what could be wrong.