Mild fever and swollen red face (esp. under both eyes) after sunburn. what's the best treatment? how long does it take to heal?

It depends on what you consider healed. Pain if any should subside in a day or so. Skin may peal for upto 10 days or so, redness should be gone in a week or two. Pigmentation may persist for months.

You may have a case of mild sun poisoning. Treatment consists of cold baths or cold compresses. Also steroid creams, oral steroids , pain meds and topical antibiotics. This can last for weeks and keep yourself hydrated during this time.