Sorry you are in so much pain! Is it only aggravated by cycling? Do you have a sense of why your right side is affected more than your left?
I would start with getting evaluated by an ortho and see if you can get a PT referral. Maybe ask around your cycling community to see if anyone can recommend a Dr. to you.
I had an awesome LMT back in Seattle. He did some trigger point work on me, when my shoulder locked up from using crutches. A couple of books I saw on his coffee table: The Trigger Point Workbook and the Frozen Shoulder Workbook, both by Clair Davies. I got the first one for myself. There are a lot of great self-care techniques in it, I imagine the Shoulder one is just as good.
2014 Bobbin Bramble / Brooks B67
2008 Rodriguez Rainier Mirage / Terry Butterfly Tri Gel
2007 Dahon Speed Pro TT / Biologic Velvet
1998? GT Rebound / Serfas Gel