Jim, there are many forms of shin splints, as you can see by searching at a site like webmd. I'd advise having it checked out by a doc, because in my case the particular type I have is not helped by stretching. Ice always helps.
Here's my biking/shin splint story: I rode a recumbent up a long steep hill (10 mile ride, mostly up) on a club ride. On a 'bent you can't stand to pedal, so to get extra power on steep grades I pulled with one foot while pushing with the other. After this ride I developed shin splints in one of my shins, because pulling uses the muscle in the front of your shins. I got it diagnosed as "anterior tibial periostitis" which means the outer layer of bone on the front of my tibia is inflamed, because that's where the muscle tendon attaches. The doc recommened ice and lots of ibuprofen. I find that with that treatment that I can get it under control, but it's always ready to flare back up if ever I overdo on a ride. Like you, mine never hurts while riding, it just gets whiny later. I can get it "unflared" in a week or so of taking it easy, and then it can be pretty quiet for months, but it never completely goes away. It's been 3 years now. I sincerely hope yours goes away sooner than that!