I get shin splints too (always have) which can be due to multiple reasons.

1.) Not wearing supportive shoes. It DOES make a difference & is well-worth the investment of $60 or so, imho.
2.) Not warming up enough. I am a walker personally, but at around 4.5 mph, which is 50% faster than "normal". So, I have to make myself walk at a considerably slower speed for a quarter mile or so, and listen to my body...slowly speeding up to my normal exercise pace. This has helped a lot. Knock on wood!
3.) You may need arch supports in your shoes. Get a test done and, if necessary, purchase shoe implants to support your arches.

According to Mayo Clinic website:
"The term "shin splints" refers to pain along the shinbone (tibia) — the large bone in the front of your lower leg. Shin splints are common in runners, dancers and military recruits.

Medically known as medial tibial stress syndrome, shin splints often occur in athletes who have recently intensified or changed their training routines. The muscles, tendons and bone tissue become overworked by the increased activity.

Most cases of shin splints can be treated with rest, ice and other self-care measures. Wearing proper footwear and modifying your exercise routine can help prevent shin splints from recurring....

To help prevent shin splints:

Choose the right shoes. Wear footwear that suits your sport. If you're a runner, replace your shoes about every 350 to 500 miles (560 to 800 kilometers).
Consider arch supports. Arch supports can help prevent the pain of shin splints, especially if you have flat arches.
Lessen the impact. Cross-train with a sport that places less impact on your shins, such as swimming, walking or biking. Remember to start new activities slowly. Increase time and intensity gradually.
Add strength training to your workout. To strengthen your calf muscles, try toe raises. Stand up. Slowly rise up on your toes, then slowly lower your heels to the floor. Repeat 10 times. When this becomes easy, do the exercise holding progressively heavier weights. Leg presses and other exercises for your lower legs can be helpful, too."