It's a tough one to answer really without having any real medical/physio knowledge...
As i'd imagine you know, shin splints is an overuse injury and not something that just happens over the course of a single run (well certainly not typically!). Perhaps a weakened ligament/tendon (I forget which is which) that has been pushed over the edge when you changed to your new shoes that have altered your running style?
Stick with your new shoes for a while though, try not to go too hard at the moment and give your body some chance to catch up and recover. If the trainers are still causing you grief a little further down the line then perhaps kick up a fuss!
