Insoles and braces and wraps for shin splints are crap. They'll just make you even weaker. Pain in the shins is almost always shin splints or stress fractures. Since you have them in both legs and haven't been overworking your legs or running much lately, they're probably shin splints. Luckily (hopefully?) you're a weight lifter, so all you need to do is weighted toe raises. I do them on the leg press machine and can do about 50% my leg press weight. Also, stretch your calves a lot, at least once a day.
There's a lot to read on shin splints, so get reading. It's probably one of the few injuries that you can safely self diagnose and self treat.
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