Yesterday, my flying partner to the Kroon fly-in did just that. Marthinus ("Slow Jet" on the forum) and I had an uneventful flight to Kroon. I had a lekker breakfast but he declined breakfast, saying he will eat later that day.
Just after take off, returning to Brits, Slow Jet experienced a gust from the side and immediately corrected. Once I was in the air I enquired about his position and he replied calmly "Over Garankua, but Roel, I have a problem ... my left shoulder is dislocated and I have NO use of my left arm".

We decided to rather carry on towards Brits where we had a better chance of a smooth tarred runway and an into wind landing. Slow Jet carried on climbing to 6000 ASL into a strong head wind (22 mph ground speed) but very smooth air. Still only flying with his right arm and his right hand on the PTT. His left arm was dangling next to him. I went ahead, landed and waited next to the runway in case he had a botched landing.
With one arm he flew his descending approach through rough and turbulent air like an ace and did a perfect landing on the grass runway next to our tarred runway. At the hangar I helped him out of his flight suite and the slightest movements made him wince in pain. In fact, at one point I thought he was going to pass out.
His sister took him to a doctor who caused even more pain without success.
Bottom line, yesterday afternoon, Marthinus found himself in a theatre in hospital, and because he did not have breakfast, they were able to put him to sleep re-locate that shoulder. Spoke to him later last night and, albeit sore and stiff, our hero aviator is fine.
Vriend, well done for handling the crisis situation in your (typical) calm and measured way !

Jy mag maar vlieg hoor !!
Viva ANC !
And not the other ANC I have come to hate
I'd love to hear of other pilot's experiences of in flight injuries and how it was managed.