I've got an athlete who got over osgoods pretty quickly. He'd had severs too, and they're basically the same thing.
Here is what you should do:
1. rest the knee from impact for 2 weeks. If you want to keep fit, do heaps of swimming and cycling (spin calsses, whatever) in that time.
2. rub voltaren gel over it every night. Smear a lot over it before you go to bed and wrap your knee in plastic, like it's a sandwich. This intensifies the effect (and stops things getting dirty!).
3. stretch your quads twice a day. The pain is from tugging on tendons around the growth plate, which is brought about from bones growing first and muscles/ligaments/tendons then catching up. You need to stretch those muscles/ligaments/tendons religiously during those 2 weeks so they catch up. The best way is to lie down on your front, and have someone lift your heel over and push it into your butt and hold for 30 secs each leg.
4. Yes when you start again there are two taping methods you can use. One is the kt-tape method. The other is the one where you use normal strapping tape and wind it into a cord. Both work and you can do one or even both. You will feel the kt tape one less when running.
It's true a little bit of pain is nothing to worry about. You can ice the area before you run to help.
You need though to get the inflammation down (hence the rest) and to relieve the strain on the tendons (hence the stretching).