The best thing is to plan ahead (certainly over 21 days / less than 120-180 days in advance). Some US airlines offer nonrefundable "instant upgrade" type fares that are cheaper than some refundable / unrestricted coach fares (of course, if your flight or flights include regional aircraft, it doesn't matter, and if it's a sparsely flown route prices may be higher anyway).
Southwest and others do offer early boarding - and in Southwest's case, that means any seat except for an exit row, practically speaking.
Of course, making a major issue of one's condition ("Yes, I have a coach ticket but absolutely can not fly unless...") could potentially result in being required to provide a "fitness to fly" certification - a backfire many would prefer not to have to endure.
The chances of an upgrade, as many have posted, based on asking at the ticket counter or gate based on an existing condition are practically slim to none, and Slim rode out of town yesterday.
