From this article, Exercise Recommendations for Chronic Fatigue Sufferers Spark Debate , comes this quote:
A study by British researchers suggests that exercising beyond the point of fatigue is one way for people who suffer from chronic fatigue syndrome (CFS) to build strength and feel better.
The overhead press can be a very productive exercise. Like any exercise, if it performed with improper form or to excess injuries may result. For those who have shoulder or back problems it might be best to avoid this exercise altogether.
From this New York Times article, Balancing Painful Swelling with a Desire to Exercise, come these quotes:
Some women living with lymphedema have managed to do repetitive upper-body exercise in a way that doesn't aggravate their symptoms.
And this quote: