If you don't suspect a fracture or soft tissue tear, you can try:

-Resting the area.
-Immobilize the painful area in a brace.
-Apply cold compress to the painful area and elevate the shoulder slightly above the heart level.

Perform these 3-5 times daily for a week. See your doctor if symptoms do not resolve.

Hard to say with that history. Most likely a stretched ligament. See your Dr. I recommend a sports Dr

If there is true pain then this likely means there is an injury, and depending on the location can range from damage to the rotator cuff or the labrum. A combination between rest, ice, elevation and topical/oral anti-inflammatories can be used with caution. If not improving should consider full evaluation with MRI/imaging to prevent a small injury from getting significantly worse.

Rest, ice, alternating with warm moist heat. Rotator cuff strengthening every other day. Stretching every day. If not allergic or not contradicted, may alternate Tylenol with ibuprofen or naproxen.