My understanding from med school is that shin splints are caused by repetitive microtrauma of one of the muscles in your leg that’s involved in flexing your foot upwards. This is caused by overexertion of the muscles, especially if you don’t warm up and cool down sufficiently. The overexertion causes your muscles to swell from the overuse, and since the leg has tight compartments, the swelling causes blood flow to your muscles to be reduced, causing pain. I’m not sure how the brace helps, but maybe your trainer is on the right track when he or she recommended that you use these muscles more, to get them used to that level of usage.