Actually for shin splints, there is a special "brace" type thing you can get, basically from any sports store. Looks a little like leg warmers, they go from your ankle to your knee. They are super tight (a pain in the rear to get on and off), but they do help.
Best things you can do? Stretch your calves and watch your form (don't let your feet *smack*, use the muscles in your legs to help cushion the impact).
<<---daughter of a track and cross country coach...
Gretch, what you are describing is the common thing for an ankle sprain. A wrap like that won't do much for shin splints.
NSAID (Naproxen, Ibuprofin, Acetaminophin, etc) are fine to take once in a while. If they aren't helping, or the pain persists with only moderate exersize, it's time to see your doc.