Shin splint is an overuse injury, usually caused by going too much, too soon. I noted that you recently started walking.
Some things to ascertain:
What is your physical activity like before you started this workout?
What is your frequency?
How often do you do this workout of walking?
What is the distance you clock during each walk?
You can try easing off ...
Your hip internal rotators may be tight and weaker compared to your external rotators. Hence, the imbalance.
I’ll stretch the hip internal rotators and strengthen my hip external rotators (glute max).
You can do exercises which encourage hip external rotation like putting a band around your knee while squatting.
Something interesting I learned is that ...