cooking oil burn on face

hi sorry this is my first post here, F20, 120lbs, 5’3 no underlying health conditions or medications

today i was cooking and accidentally splashed my face with hot cooking oil which burned the skin around my upper lip and cheeks, i went to the er and they told me it was a first degree burn and prescribed silver sulfadiazine

however i read that burn usually take a while to show the actual damage, which means that my burns might progress to 2nd degree which worries me, and also the fact that i read that silver sulfadiazine is not actually that effective against infections, which is my main concern

these are pics from my face the 1st pic is from rn, about 10 hours since i burned my skin and after going to the ER, the 2nd was my face otw to the er and the 3rd was right after it happened. at first i ran my face under cold water and applied aloe vera to it, then the er dr applied a gauze with silver sulfa on it, after saying it was pretty superficial and a first degree burn

my question is, is it actually a first degree burn? because it looks to me like a second degree one…