Even if it's a small burn, do go to hospital if it's a chemical burn.
I think those 25% and 10% boundaries might be wrong there. Your palm is roughly 1% surface area.
I went to minor injuries with a burn and got seen to pretty quick. Mind you, a flashbang had exploded under my hand and burnt the first couple of layers of skin around my thumb off. Wasn't the best experience of my life. Something like, "Sorry, there's no on-call anaesthesiologist. I'm going to cut the dead skin away, and you can tell me when it starts to hurt so I know to stop cutting."
All healed up nicely now though.