Nike Frees are ok for shin splints involving the front of your shins (anterior shin splints). Since you got improvement with a more stable shoe, I'm guessing you have shin splints involving the instep (posterior medial) side of your shins. In this case an anti-pronation/motion control shoe might be best for you until your condition resolves. For some of my patients, I even add a wedge in the heel to control the pronation further.
The Frees would likely make your kind of shin splints (posterior medial shin splints) worse. BTW I own a 2 pairs of Nike Frees, and have performed running gait analysis while wearing the Frees, so I am not an "anti-Free guy".