First, one ground rule: never wipe the crumbs off of a burner with your hand. Never mind that you didn’t realize it was just used a moment ago to boil water for somebody else’s tea. What were crumbs doing there anyway?
But you’re in a rush, so I’ll get to the remedy straight away.
Make a paste of baking soda and water. It should be pasty, not liquidy.
Put a thick dollop all over the burn and keep it there for a few minutes. It will work rapidly to cool the pain. Each time you feel the pain returning, reapply the paste.