I have a swollen area on my posterior upper left shoulder (where the top of my humerus is). it slightly stings/burns, could this be a tumor?

Unlikely: More often than not, tumors do not cause pain or tenderness. However, if you have a lump that you can feel on your shoulder, you should absolutely see your doctor and have a complete physical exam.

Not likely: A painful mass in that area is more likely to be an inflammed sebaceous cyst or a lipoma which is a benign tumor. Obviously, a sarcoma or other malignant tumor is a possibility. You should have it checked my a physician.