Hi grade undersurface distal supraspinatus tear now spasms from shoulder to neck/arm pit. Arm feels heavy numb & burns prescription inject & p.T. Is this normal?

Might be. Certainly pain around shoulder girdle can be related to partial undersurface ss tear. Rx is initially cortisone, antiinflamms and pt. Numbness and burning may or may not be related. These are more neurologic sxs and have to r/o cervical radic, thoracic outlet and peripheral nerve impingement.
No. I would not say it is normal. Rotator cuff tears can certainly cause shoulder pain and difficulty using the arm, but do not characteristically cause arm numbness. It sounds like you might also have something else going on, potentially a problems with the nerves in the neck. You may want to get an MRI of the neck to look for a disc herniation or area of impingement. Thanks for the question.