What should be done for sprained ankle that is not painful or any swelling (feels slightly "off")?

Many options: Is this an acute sprain or joint instability after a sprain from the past? Rest, ice, elevation are good for acute. I like to use quercetin or turmeric as well to reduce inflammation. Wear supportive shoes or a brace/wrap at first. A chronic joint instability might be improved with rehab exercises and perhaps prolotherapy.

PT: Best to to see a pt to strengthen the muscles on the outside of the ankle to restore stability.

Get it checked out: A sprained ankle is not to be taken lightly, as it can create quite a few problems for you later on if it doesn't heal properly. Please visit a podiatrist at your earliest convenience for a thorough evaluation.

How long: Even though you do not have pain or swelling, if the ankle feels unstable or abnormal when moving the ankle you should be evaluated by a physician. Most likely a course of therapeutic exercise and proprioception will improve the symptoms, however, fracture or loose body should be ruled out through a history, physical examination and possibly xrays.