Any recommended medical centers for someone who has neuromicrosurgery at C5/6?

With regards to your concern, there are many good sports clinic in America but unfortunately, we have no knowledge of which of those can serve you better. You may try the Mayo Clinic and check their reviews for more information and guidance. Meanwhile, you can treat your right shoulder pain even at home. Apply hot packs for 20 minutes everyday to relieve the pain. Start some mobility exercises to keep you mobile and flexible. I also recommend seeing a Physical Therapist as you may need more and deeper heating modalities to address your stiff joints. You can also check these links for some helpful exercises:

http://exercisesforinjuries.com/4-simple-neck-and-shoulder-pain-relieving-exercises/

http://exercisesforinjuries.com/3-shoulder-pain-relief-exercises/

https://www.facebook.com/healingthroughmovement1/videos/2040759456136378/

https://www.facebook.com/healingthroughmovement1/videos/2122005858011737/