Shin, then knee pain 1 day after running

RICE:

Rest
Ice
Compression
Elevation

Take a few days off, ice the injured area, keep the injured area compressed (compression socks would be great), and elevate your leg when you can. You'll probably be fine in a week or two at most. Nearly everyone gets a minor injury at some point, don't let it get you down. If it's still hurts in a week, or doesn't seem to be getting any better after a few days, talk to a doctor. If you are able to, do some cross training: Biking or Elliptical if your knee doesn't hurt on them, or maybe swimming. If it hurts, stop doing it and either try something else or skip the cross training.

Have you been fitted for shoes at a proper running store where they do a gait analysis and foot measurements and all? If not, you should really try to do that, the right shoes can make a huge difference in preventing injury. The other common way people injure themselves is adding to much mileage to fast. Try not to add more than 10% to either any individual run, or your weekly total. Obviously it's hard to add just 10% to short runs (going from 3 to 3.3 miles on Wednesday is a little weird), but you should be fine adding half a mile or a mile to short run all at once. Just don't add a mile to three runs in a given week, or three miles to you long run all at once. Definitely follow the 10% on weekly mileage.

I have bad knees so after I run I go home and ice then for a period of time then soak them in hot water to re leave the pain as well as rest my muscles. Do not over exert yourself if you feel pain because you will make it worse. If you still have pain a couple days after running please go to your doctors to get checked out.

I'm going to rethink my choice in footwear (even though I don't have any foot/gait problems).

I hate to badger, but you have had your gait checked and they told you that you had no gait problems? Or you're not aware of any problems with your gait because your gait seems fine to you? I ask, because lots of problems with your gait are essentially invisible to you. You can't watch yourself at ankle level from behind while you run. Problems like over/under-pronation slightly inward or outward facing toes, etc are nearly impossible to see for yourself. They're also not really going to affect the day to day life of a non-runner so that you'd notice them. They only become an issue when you're pounding your feet for 12 or 15 or 20 miles a week.

If you've had a professional gait analysis by a running store or a medical professional already then sorry to bug you about it; but I'd rather have told you something you already know than see you hurt yourself again in a few months. Gait problems are probably the single biggest cause of running injuries, and they're mostly correctable by wearing shoes designed for your particular brand of weirdness. In fact, even calling them gait "problems" is a misnomer. You could have a neutral gait (i.e. no gait problems) and be wearing shoes meant for someone who over-pronates (now your problem-less gait is a problem).