i ,yself have had a collapsed lung at the age of 15, i am now 18, i play football for 2 teams, mens and under 18's. i can run fine, i can still do the things that i used to do before the operation etc. I spent 6 days in hospital with a pipe in my chest before Hull Royal Infirmary sent me to Leeds were they operated on me straight away. they said dont do any sports whatsoever until July (this was said in february) however, my urge for sports and wanting to just kick that football caused me to start playing football again in April! there was no problems whatsoever and im completly fine now.
The doctors said you cant deep sea dive (oh well i dont live swimming anyway!) they originally said you cant fly on an aeroplane but i dont fear this is true (i havent flown before anyway and probably wont do) and they told me you cant go no faster than 70mph in a car, which was a weird thign really as 3 months later i spent two laps in a ferrari enzo round a track going 140mph! plus ive drove myself in lessons down a motorway at 70mph so thats complete nonsense.
Your son shouldnt worry about running, if it is hard to breath for him then maybe consider asking for a scan, ct or something, just to check again. Diving shouldnt be done because of the pressure on the lungs etc but running, football, etc should be fine.
oh, one other thing that has effected me after my operation, when i fall over, like in football. before i would take the fall on the chest and be unharmed, now though, without realising, i fall and instantly turn to land on my shoulders, this is just instinctive now and i cant not fall, dive into water, or slide in water parks on my chest as its instinct now to turn away!