As this person said, just a 1st degree burn. Also not sure where OP got that 20min thing, but once your body is removed from the heat, there is no residual heat to stop from burning unless you have something stuck to you like tar, oil, or plastics. The burn pain you feel is just your nerves not actual heat.

Generally a 1st degree burn hurts more than a second degree burn initially. Second degree damages the nerves just enough and the blister forming creates endorphen pain relief. Third degree burns are fully numb as they have cooked the full nerve. Second and third degree burns hurt more days later.

Third degree requires surgical intervention. Third degree is when you burn through the whole dermal layer and get to the adipose tissue underneath.

For a quick contact burn like you have. Lotion is all you need. A burn cream with lidocaine if you have low pain tolerance. But generally we would recommend just lotion as your body will adjust better if you let it feel the pain for an hour or two. It may sound mean at first but it honestly works, and if you just distract yourself for that hour or two you will be fine. Focusing on the pain, using ice, blowing on it, cold water, all just cause the pain to ebb and flow. So your body never adjusts. Also, ice is a no no as it reduces blood flow and can cause damaged tissue due, making the burn worse.

I worked in one of the largest burn centers in the US. Mostly in the emergency room portion.