I've been teaching fly casting for many years and have worked with many people who develop arm/shoulder pain after casting for a while. In nearly every case the caster was casting MUCH harder than necessary. Sometimes because the loop was big and a lot of power we necessary to get it to the target, but often the loops were good, but going much faster than needed.

Done with good technique there should be little strain on the arm/shoulder when fly casting. Very heavy gear would be an exception, of course. I'd suggest trying to cast the line as slowly as possible and concentrate on making tight, efficient loops. We've been able to very scientifically measure the energy used by casters and find that talented casters normally use about half the energy to make a cast that average casters use. If you reduced the force applied by half I'll bet your shoulder problems would go away.
Bruce Richards