Are shin splints due to low estrogen?

No: Shin splints can be due to a number of stresses on the medial tibial region of the lower leg. I wonder if your question is stimulated by the fact that some female athletes (who may get shin splints) have low estrogen levels associated with low body weight and fat content. But the low estrogen is not the cause of the muscle pain.

No: Shin splints are a mechanical strain on the insertion of the muscle into the anterior crest of the tibia and can be caused by overuse but also abnormal foot positioning such as seen with flatfoot endless.