Stretching your hips–or, for that matter, sport stretches in general–isn't going to help you much with this particular issue. The stretches you'll need to do are much more specific. General sport stretches target general groups of muscles. You'll need to target specific ones, and in specific ranges of motion to help address your problem.
Of course, we're assuming you even have shin splints. Based on the entire conversation, that certainly seems like your best bet. But keep in mind that internet voices can't accurately diagnose.
Foam rollers are your friend too.
While i agree with the above advice, the term "shin splints" is a bit vague imo.
Exercise related lower leg pain is usually periostitis, tendinitis, compartment syndrome or stress fracture.
Defining the nature of your shin splints is in your best interests.
Stress fracture is the most problematic, with the exception of rare instances of anterior compartment syndrome complications.
Regular inflammation issues should subside with RICE.
Stress fractures are sensitive to vibration (thus the heel thump and tuning fork tests) and will not "warm up" as the workout progresses.
I have a client who finished a marathon with the right inf. and sup. pubic rami fractured and thought it was a muscle spasm for days afterwards, until she finally got imagery done, lol.
So it is certainly possible to have one and not realize the nature of the injury.
Of course i've also known coaches to cry "Stress fracture!" in order to bench an athlete in pain, even if there was no formal diagnosis.
Prudent, if a bit misguided.
I don't know how to target those specific muscles in my stretches, though.
If it doesn't work, I'll just assume it's not shin splits and go on to the next thing.
Here's a good resource: