Originally Posted by FlippingHades
If weight on the right shoulder hurts the left occasionally, I'd say your best option is a rack and panniers -- don't take any chances!
Or, if $$$ is a problem, get a rack and bungee cords. You can strap your backpack or messenger bag to the rack. It won't be as stable as panniers or, probably, as watertight, but it won't be as expensive.
As to whether the messenger bag over your shoulder is safe, don't do it on our advice. Ask the doctor who treated you. The doctor is the only person who should tell you when that will be OK.