Aloe vera, right away...
Here's a rule of thumb: ALWAYS have a live aloe plant handy RIGHT IN THE KITCHEN!!!
I've had mine for 8 years - so long that it's given me multiple babies and flowers (a lot of people don't even know that aloe flowers - I didn't until the first time that happened - but it takes something like 4 or 5 years!)
Aloe is by far the best skin remedy for any heat-based irritation - burns, scrapes, and even poison ivy/oak. Though it will work throughout the duration of the injury, the sooner you get it on there, the better.
My daughter (now a teen) had an accident with boiling water when she was 4 years old... an old Pyrex bowl split by the bottom seam when it was full of boiling water, splashing off the table and onto her in her pajamas. It got her on the back side of her left forearm and her left thigh. I peeled off her pjs right away, put cool water on it for a few seconds... and when that did nothing to help (the water had literally peeled away a few layers of skin immediately), I cut 2 huge leaves from the plant, slit them open, and just placed it on the burns. We took her to the doctor immediately, with the aloe basically held onto her leg and arm by bandages.
The pediatrician said that was the BEST THING I could've done, and it probably prevented the need for a lot more serious care... though she did have to go through daily dressing changes at the dr's office for a week, today (9 years later), even though the burns covered a large line on the back of that forearm and basically covered the front of her left thigh, she has NO SCARRING AT ALL!
I've used it as the onset of poison ivy, too... and it works! Like I said, almost anything that is a heat-producing skin irritation.