Shin splints is the classic injury for enthusiastic people who see aerobic improvements that outpace the strengthening of muscle, tendon and bone. Shin splints is almost unheard of amongst experienced runners.

It's fantastic that squats helped you, but if you are primarily looking to improve your running then months of training at a lower intensity, to avoid the shin splints, is much more productive than stop-start training resulting from the need to let your injury heal.

I got shin splints because my calves were too strong, so I worked on that issue of strengthening the front, and flexibility.