It's just one of those things that you'll have to deal with. I would suggest getting a few zip lock baggies (about quart size) to take with you. You can put some baby wipes and sanitary supplies in the zip lock bags and put them in one of your many pockets on your uniform. The reason I say to use a zip lock bags is because the baby wipes will dry out, and during some of your training you could get wet and dirty, and nobody wants soggy sanitary supplies. The baby wipes are great for cleaning up, especially when you do field problems and have to camp out in a tent for a while with out any showers around.
If you have a problem with cramps, you will have to go to sick call to get any meds for that. During basic training they do not allow you to have any medication that has not been prescribed to you by a doctor to include any over the counter medication.
If you are like me, you may not have to worry about it at all! During basic training, due to the added stress and sudden extra exercises and weight loss I missed my period. That is the first and only time I have ever missed my period, other wise you could set a clock by me. You may also be able to get birth control that will keep you from getting your period so you don't have to worry about it at all.
Good luck.