Regardless of if there is no PRT with your recruiter, you should show up to OCS in TOP physical condition. My only guess is that they want to prevent injury before OCS, but you should make YOURSELF test YOURSELF on the PRT. Go out to a track and practice the PRT a few times. One thing that helps me is to run with our ROTC groups/soccer clubs at college. Engage yourself and motivate yourself; you're going to a leadership school and you should already have the basics to becoming a leader, one quality of which is to initiate things yourself.
Shoes shouldn't matter. Though you want to show up to OCS with a quality pair of shoes, the best training I've ever done in my life is barefoot on either a track or on ground (that obviously isn't littered with glass as this could cause problems). It'll hurt the hell out of your calfs and feet, but the conditioning will toughen you up to be able to run and perform in any condition and with any quality shoes.
If anyone is worried about shin splints coming up again at OCS, I've been told they probably will. I would talk to your recruiter and have your date pushed back because you don't want to get there, get injured, and spend 6+ months there in holding company.
Bottom line: run. run a lot. 3+ miles 4 days per week to get ready. Don't just slow pace it either, vary your workouts up with sprints, winders, and long stretches of hills. You want to be prepared for EVERYTHING. Don't go into it with the attitude that "just barely passing" is still passing. THis is your chance for the DIs to test you, but it's also your chance to test YOURSELF.