I've been running competitively since I was 12, and am all too familiar with them.
The three most common causes that I've experienced and had my trainers explain to me:
-Too far or too fast too quickly.
-Failure to warm up or cool down and stretch after a run (not just calves- everything)
-Improperly fitted shoes
The last one is extremely common, especially in newer runners. If you over-pronate and run in a neutral or supinator's shoe, you are
begging for shin splints. Similarly, if the shoe you are wearing is too narrow, you're asking for trouble; or even wearing a shoe made for pronators that just isn't supportive enough in the arch. Go to a running store (not a sports store, a running store) and have them evaluate your stride and foot strike. You
may be able to eliminate your problem with a simple change of shoes.
You can most definitely still run with them (I've battled them the majority of the last 14 years, as well as many of my teammates), but try and take it easy on speed and increase distance slowly (general rule of thumb is to not increase your weekly mileage by more than 10% per week). Don't even worry about speed. You don't need it for the academy. Just finish your distances. When you do run, try and do some dynamic stretching/warm ups first, and then start your run slowly (your first mile or two should ideally be your slowest of the run).
Typically the shin splints will be achey and mildly painful/discomfortable until they warm up. If they cause you significant discomfort throughout the entirety of the run, take a couple days off and just do some strength training.
Wrapping your shins will help with the pain during activity (some people like KT tape, others prefer a tight ace bandage or actual athletic tape and prewrap).
Search for preventative strength training for shin splints (typically done with resistance bands or a towel). These seem to help quite a bit if you stay consistent with it.
There are videos on techniques for massaging your shins out with ice. Whether you try this or not is up to you. I've done it for as long as I can remember and it works great. Forewarning though, it hurts like hell.
I also have a sports massage therapist who specializes in Active Release Techniques. That guy/that stuff is magic, and it typically only runs 40-50 per session, with three sessions usually entirely eliminating the problem (not just MTSS, but just about any running ailment). That may be a bit more than what you're looking for, albeit it will help.
I didn't intend on belaboring as much as I did, but I could talk about any and all aspects of running for hours

Hopefully you find at least one piece in here helpful.