If he were human and I didn’t have sylvadine or some other doctor recommended ointment, and it didn’t seem infected, I would keep it clean (and dressed to protect it (if possible)) and not do anything. Fats can make it hurt worse. If the burn is fresh they can exacerbate the damage, but it sounds like you’re past that. If you do use any commercial ointments, make sure they do not contain pain killers. Analgesics can be dangerous to chickens, so best not take any chances on them with your cockatiel.
From what you say, it doesn’t sound like you need to worry too much over the burns. He should heal up on his own. His poor little broken heart might be another matter. It may be advisable to eventually consider getting him another companion, even if not a sweetheart, but my knowledge of cockatiels is at best limited.
I can't find any of the medication, stupidly. I'm right in the middle of packing to move countries, so it's a mess.

I do have to run to
Walmart today. Maybe they might have something? It resembles a wound on his poor toe. He's not picking at it, luckily.
Ugh. I feel useless. All these suggestions and I keep going "nope. Nope. Nope." Promise I'm working on taking care of him, not just making excuses! Today I'm going to disinfect his cage to the best of my ability for germs. Prying him out of the cage is a pain at the moment. I'm ashamed to say I'm putting it off. If I have to I'll park on
Walmart's floor with my cell and research the entire pharmacy area. I feel bad enough that I missed the burn the first time around.
His broken heart is slowly healing, luckily. He's freaking out still (will NOT leave his cage) but managing. I got a lot of advice for how to deal with that. He's been listening to bird song, getting treats, lots of bonding time. He's stopped screaming finally!

I have a parakeet that will end up keeping him company. A cockatiel buddy isn't a good idea at the moment. My husband is dying of brain cancer, hence the country moving. I wouldn't be able to give them the love they deserve. Giles is lucky he can stay with my Mom, who he also loves.
We put up a curtain between the living room, where he stays, and the kitchen, where he wants to become BBQ dinner. We also put up two curtains by the front door - one inside and one outside - so he won't escape again.