^^^ you can try acupuncture treatments to help alleviate the swelling. apply a lot of heat as much as possible. and after your runs ice it down
also run on grass on flat surfaces. try not to run downhill. your shoes should be well fitting and new, don't run in worn shoes.
when you run try and keep your feet forward, so when you land they are not angled outward, that can strain your shins. and also you should be aware of heel striking when you run, don't do it, that is a fast way to inflame your shins. always land slightly on the front of your foot and keep your strides short like the way a bird runs. kinda like RPM's in a car, you want short strides. record a football game or track meet on tv and watch when they are sprinting how they strike the ground.. they don't land hard, they land on the front of their foot with short quick strides. nfl athletes have god given talent and they naturally are able to glide when they sprint, track stars do as well, but they are also taught to run like that.
and final tip you can try is run barefoot. I have a sneaky suspician that the #1 reason for shin splints is shoes, its just like wearing gloves when you workout, it effects forearm development... well running with shoes might have the same effect on the shins.. just a theory i have cause i worked out with gloves and started to get forearm splints the same way i was getting shin splints, when i stopped using gloves after a few weeks the forearm splints went away. you might want to try running barefoot or get those shoes that you wear which are almost like being barefoot. i think nike sells them.
after you are done with your navy test then stop running and if you need cardio do bicycling instead for the time being and let them heal back up.