Understanding shin splints requires knowing how to use your foot muscles properly. This affects all your ballet positions and movements. Even more basic, is understanding where your weight should be on your standing foot/feet. If not drawn back too much on the heel, the calf muscles and tibial (shin) muscles do not have to strain even before you've made a move. To avoid shin splints altogether, check how you're standing in parallel, and how your feet are positioned on the floor.
Ideally, you have arches that don't flatten on the floor when you are standing, and also don't hold an arch shape with a rigid locked position. The front of your ankle is relaxed because your weight is on the middle of the heel, the outside of the foot at the little toe metatarsal joint, and the inside of the foot at the big toe metatarsal joint.
The rest of your body is stacked upward from ankle to knee (if your knees are hyper-extended you have been shown how to hold them in a straight position) to hip through the natural spinal curves to your head. Imagery-wise, your head floats above all of this. Realistically, you work with your rib cage held but not clenched down, so your neck does not have to compensate with a chin pulling up and forward, eliminating the natural curve.
And all of that has to do with how your feet rest on the floor.
If your feet are flat and soft, standing correctly, turning out correctly and getting the weight distributed on the foot (picture a triangle or tripod) is going to activate the sole of the foot muscles but NOT activate tibial (shin) and/or calf muscles that will strain if your weight has sunk inwards. Dancers call it rolling ankles.
Having the weight a tad forward (isn't that nice and scientific) feeling ready to move into a tendu and take the weight on the standing leg, is an activated but not tense or clenched feeling in your legs and core muscle area.
So even though shin splints are usually associated with jumping on hard floors, or overworking through long rehearsal days, shin splints can start with a lack of understanding just how to stand on your feet - and also not understanding what type of feet you are standing on.
It doesn't MATTER what kind of feet you have. It matters that you know how to use them and improve them, way before you get into pointe shoes.
A foot that is arched but rigid in the mid section can be loosened up with massage, warm foot baths, and regular ballet strengthening exercises.
A soft flat foot can be strengthened and activated properly on the floor.
A hyper-mobile highly arched foot can be strengthened and controlled by the intrinsic (sole of the foot) muscles.
A less flexible ankle can be stretched properly, starting with relaxing the shin muscles.......that may be strained by weight drawing back on the heel, as mentioned above.
Ideally you prevent shin splints. If you are past that, you practice good care of shin splints with massage, ice, perhaps rest, and applying all of the above. Swelling and inflammation of the tibial muscles can get extremely painful, and severe pain should be addressed by a ballet/sports/fitness physiotherapist or chiropractor. There may be a stress fracture present, so it's good to know exactly what you are healing.
Take a look at your parallel bare feet position in the mirror and get your weight placed properly. Women and men in sports/fitness/ballet can learn how to build your foot muscles for fine reflexes, fine balance, and for ballet pointe shoes.