How long does it take for facial swelling to go down after a laser peel?

Depends... ...On how aggressive the peel was, more than anything else. Superficial peels with erbium:yag lasers typically heal in a few days, while deeper peels with more powerful lasers may take a week or longer. Fractional laser treatments sometimes take even longer than that -- depending, once again, on how aggressive the procedure was.
Few days to one week. The facial swelling or edema after a laser peel can last anywhere from 3 to 7 days, depending on how extensive the treatment is. At my practice, we are able to make patients comfortable after their treatment by prescribing a short course of prednisone, so long as their are no contraindications to them taking the medication.