My shoulder has been hurting really bad. I dobt have full rotation and it hurts to raise it. Could it be bursitus or arthritis?

Yes. It could be both but arthritis is a chronic condition that occurs over time. Only an exam by your doctor can give you a definitive answer.
Rotator cuff. This could be a rotator cuff problem. This could be a tendinosis or a year or other injury. You need to have this evaluated. Arthritis is always a possibility but i would look at the other issues first.
Shoulder stiffness. Shoulder pain can limit movement. There are many causes of shoulder pain. This is different from true stiffness of the shoulder. The 2 causes of true loss of passive range of motion are glenohumeral arthritis and frozen shoulder. An x-ray can differentiate the 2.