How exactly did you call him out on it?

Ignore him, honestly. If he knows he can get under your skin, he won't let up.

I just said "you should shut your fucking face"

I'm sure I would have said something similar. The problem is if you go to a teacher now, they can bring up your reply which will probably place you in some trouble as well.
Two ways to deal with it, ignore it like the person above suggested, or figure out some of his insecurities and attack those. If he uses the same term again feel free to question his originality.
If it happens again, I hope you have an ally that over hears it so it's not just a he said, she said.
In the mean time, something I've found helpful: I correct people who insult me. I make the insult better, and then tell them if you're going to insult me you might as well do it right. It infuriates people!

Buddy, I am in the same boat.
This kid won't stop staring at me, shaking his head when I get something wrong, saying his near negative IQ is smarter than mine(I believe myself to be one of the smarter people), has an ego that could crush a planet, and tries to give me "swag tips"(Basically they're just insults on my clothes just because I don't wear what he wears[the egotical ass literally wore his face and his name on a fucking hoodie] or talk how he talks)

Alright anyone who gets offended by someone using their race derogatively needs to hang around me. I'll teach you to do the ching chang chong back so hard they'll shit themselves inside out.
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Lesson #1
Whip your head around real violently and look them in the eyes (or where their eyes would be if they aren't facing you) and make various angry noises that sound vaguely like whatever they insulted you.
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Example 1: Chinese
CHING JU DAO LAI! JAO MEI HUANG DI FAHNG JONG CHING. CHONG HAI! CHONG HAI! JA BOO MEI, DAO LA! NI DAO LA?! HAAAA?
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Analysis: First you have to make the angry noises sound like you're insulting their ancestors, their cow, and their pimply face. Then you progress to repeating the same few syllables to make it sound like "WANNA FIGHT ME? WANNA FIGHT ME?" until you deem it to be enough. Then you do a bit of verbal chest puffing. Use your imagination.

Oh my god I did that to a chinese kid once and I only got in trouble for disrupting class because it was a widespread belief that black people can't be racist

See that's how you use race in your favor. If someone racism's you, feel free to smash back.

Now, this advice won't work for everyone, but if someone used my race against me as an argument I would break their nose. Once again, not for everyone

Depending on who and where you are you could stand a fair chance of a battery charge.

Ah well, in my honest opinion it'd be worth it. Someone doesn't insult my nationality and get away with it

Someone insults my nationality and I insult it even more

I'm sorry, Chu, but I'm too proud to insult my race. We're only so few.

What are you?

Hmong

Are we having an Asian talk?
Can I join?

ho mihn chi

It's 'Hồ Chí Minh'
And you know him?

no