It could have something to do with over-development of some muscles and others not being under used. It was also suggested somewhere that unicycling especially with short cranks shorten your leg muscles due to the repetitive nature of pedaling and using a relatively small range of motion.
In high school while on the track team I got shin splints. I solved it by stretching my calves, achilies, and ankles (kneel w/ shins on the ground and sit on your ankles) and strengthening the muscle in front of my tibia (toe raises w/ an ankle wieght staped to my toes).
I got shin splints back when I ran CC and track in HS. Take IB prophin before you run or unicycle as the case may be. Unicycling shouldnt affect it as much, but wrapping your arches is a good thing. Heat up wet towels and put them on your legs before you run. Stretch, something you should do before any exercising including unicycling. And ice your legs after. If its really bad you might have to just sit it out for a while so they can get better. Either way IB prophin will help. Best luck to you