Do I have a rotator cuff injury or is it just a pulled muscles if I have a strange loose sensation when throwing?

Painful throwing. Shoulder instability is defined as the presence of symptoms associated with laxity (i.e. "looseness") in the shoulder. It can come from a variety of causes, including weakness of muscles in the shoulder and shoulder blade, overstretch of the ligaments, or tears in the labrum (cartilage around the socket). An accurate diagnosis is important before beginning treatment. Good luck!
Possibly. However, if your shoulder feels loose, you may have shoulder laxity. This may be treatable with strengthening and physical therapy. See an orthopaedic surgeon for an accurate diagnosis.
Could be. You could have a strain of the rotator cuff, or you may have some degree of shoulder instability. See a sports medicine shoulder orthopedic specialist.