Burn question - do I need to see a doctor?

Do I need to see a doctor or can I treat my burns with self care?

What degree burn do I have?

I accidentially picked up a very hot pyrex bowl (was sitting in a 500 degree oven for 30 minutes). This was ~48 hours ago (7pm Sunday Central time)
-Burn areas are small (largest is 1 inch x .5 inch)
-Burn areas on 4 fingers on left hand, 2 fingers on right hand (thumbs, middle fingers got it worst)
-Pain lasted 4-8 hours, and then pain stopped
-Burn areas look waxy white and skin is a bit leathery/thicker ?
-A little bit of visible blistering, but not a whole lot
-I saw went to a clinic at work and the lady prescribed silver sulfadiazine cream and to keep it uncovered unless the blisters start to leak.

Are there any potential long term effects? (Do I need skin grafting or anything like that?)

Thanks!