What can you do for a painful shoulder - likely rotator cuff? I don't know how I injured it.

Try ice/ antiinflamm. Intially, would suggest relative rest (no heavy work or lifting, stop weight lifting, sports using the shoulder), ice for 15-20 minutes nightly the entire shoulder area with flat flexible soft ice pack. Alternate with heat application, or topical like aspercreme, icy-hot.... If tolerated, may try two advil (ibuprofen) or one to two alleve daily with food. If problem persists more than 10 days, see doc.
Diagnosis? Shoulder pain can have many sources and we need to first establish the cause for your shoulder pain. If rest and over the counter options have not helped see a doctor for an evaluation. Learn more about shoulder pain here: http://theshouldercenter.Com/shoulder-pain.Htm.