personally in the first few things that come to mind warfarin would be under point 100 on the list. I've be very interested to see that article you found.
I did however have shoulder issues post surgery and that is caused by what they do to you during surgery to make the access better for the surgeon. Everyone I've spoken to (meaning in person) who has had any sort of shoulder issue has had some sort of "frozen shoulder" issue emerge after surgery.
I'd "finger" that as the cause first.
As it happens I can't sleep on soft beds now (meaning since my 2nd surgery) without my shoulder going to sleep. I moved to a proper cotton Japanese futon back in about 1994 and never looked back.
Definitely sleeping on one side is better (for me its the left).
Still, I'd love to read that article about warfarin you found. I've never seen a drug more maligned by the less qualified than Warfarin. President Truman was in office unti 1953 and as such was one of the first high profile warfarin users. So now nearly 70 years later we only have murky shakey fluffy bullsh1t articles maligning warfarin, and you can bet your your bottom dollar that the makers of modern (more strokes and deaths than warfarin) drugs would be all over every actually provable side effect of warfarin ... interestingly they haven't managed it yet (despite great financial backing).
Best of luck with the shoulder ... have you seen a good physio or chiro?