Shin splints are stress injuries, and oyu should most assuredly not "power through them." That's a great way to get hurt! Untreated shin splints can turn into stress fractures. If you're having them, something's not right. Either the shoes aren't working anymore, your form's off (overstriding is a common problem, especially on the treadmill), or you're doing too much, too soon.
You can do something, and should. :) It's primarily about prevention, but don't ignore this pain... it's your body trying to tell you something.
Runner's World did a FANTASTIC video not long ago about shin splints you need to see! www.runnersworld.com/injury-prevention-rec