What could be possible causes of my right shoulder tightening/contracting when i begin to walk?

Get it checked: Might be simple cause as having muscle spasm when using the shoulder muscles with the swinging movement of the arms during walking Or it might be an indication of something else like heart trouble, like angina. It is less likely being on the right shoulder but still a possibility

Possibilities : These are many possibilities: arthritis, muscular problems, sprain and so on. Need to have more information and evaluation of your shoulder for diagnosis. Can be treated with physical therapy pretty good.

Usually muscle strai: Typically this type of pain with activity involves a muscle strain. If these symptoms in your shoulder blade (back of your shoulder it is likely the muscles in your upper back. Consider heat/stretches. If it doesn't improve physical therapy may help after having it evaluated by a physician who specializes in sports/orthopedics. Hope that helps!