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It would help to have some detail applied to the question. “Beaten up in a fist fight” can cover a lot of ground, and even though I’ve never been in an honest-to-gosh fist fight in my life (nor punched anyone since I was in single digits in age), there’s a lot that I know about this from observation.
First of all, the Hollywood depictions of knock-down drag-out street and bar fights that last for minutes on end are total nonsense. Most “fights” of this sort are over within one or two punches. A punch that puts someone on the ground is usually all it takes, and that can be accomplished – by someone who knows what he’s doing – with a single blow. Check out YouTube videos of bouncers handling unruly evictions from a bar, for example, or drunks who decide that they want a piece of him: one punch, turning the body into the punch and driving with the force of the body behind the shoulder, and it’s over.
Of course, not everyone on YouTube videos knows how to throw a punch. Many people simply swing wildly, and / or with the fist not closed tightly or straight into the head or chin, for example, and are surprised that their hand won’t work afterward for some time because they’ve broken the wrist, a knuckle or two, or one or more fingers. I’ve had a broken toe; I can only imagine the pain and lost mobility from broken bones in the hand. And that’s one of the things that @Muad_Dib was referring to: even the winner of a fight who has punched incorrectly to a hard surface has a banged-up hand or two.
Body punches hurt for days, but sore muscles and bruises don’t put one out of commission, they just lessen mobility and good feeling.
If you’re talking about organized boxing, then that’s another story altogether. I’ve never done any boxing, either, but I’ve watched a few on television. Those guys get beat all to hell, too, but usually their hands (and therefore their other bones, too, as a rule) are not so badly injured. But facial and body bruises and cuts (especially to the face, in that sport) take time to heal, and the day-after swelling can be especially sore. Part of the reason for that is that the sport is refereed, so that there are no “killing blows” (as a rule), and the mayhem can go on for as long as both fighters are willing and responsive. That generally wouldn’t happen in a street fight, where “fairness” is not part of the “game”.