These are some nicknames that apply to all because of your water quirk:
~guppy
~Riverdance
~the healer

ALSO!!!

Majesty is a neutral term for any royal title! So feel free to replace majesty with Queen/princess or king/prince if you prefer it gendered~

They will also call you any nicknames you prefer, so feel free to add them in this section right here via comments~

Deku

His: broccoli bean, Zuzu/Zuku/Izu, mini might
Yours: dog tamer (coined by Denki and it stuck), his powerhouse, his life

Todoroki

His: icy hot, Prince Charming, lord oblivious
Yours: his infinity, precious, darling, beloved

Bakugou

His: porcupine, hedgehog, yuppy puppy, king
Yours: the chihuahua, gorgeous, majesty, saint

Kirishima

His: boulder boy, daddy shark, chomper, double R
Yours: pebble, mommy shark, sweetness

Denki

His: Pikachu, bolt, Sir Flirts-a-lot, derpy, lightning bug
Yours: hot stuff, sweet cheeks, his little outlet, cutie pie

Iida

His: Sonic, king, Mr. Class dad, robo cop, knight
Yours: gemstone, beloved, darling, his love

Sero

His: Meme lord, Mr. MaryJane, your loving latino, future
Yours: his salsa dancer, the name of your favorite candy, his love

Koda

His: you're not big on nicknames, so you either call him teddy bear or sweetie
Yours: he only calls you buy your name unless it's a special occasion. If that occurs, it's normally guppy.

Sato

His: stud muffin, hot crossed buns, cake-for-days, any baking pun you can come up with
Yours: sweet tooth, cavity, pumpkin

Shoji

His: octodad, machamp, lovely
Yours: he normally calls you by your full name unless it's a sexy times. Then, your his naughty nymph.

Ojiro

His: hunky monkey, Taekwon-woah, dumpling
Yours: Angel is his normal name for you, along with the other nicknames at the top or some one off nickname

Tokoyami

His: shadow prince, my chemical crowmance, black parade, pretty much any bird pun with classic "emo bands" as the class calls them

Shinso

His: brainwave, mind fuck, sleepy kitty, sleepyhead
Yours: pillow, soft kitty, coffee machine, alarm clock, cuddle bug

Tamaki

His: shy bean, prince, beautiful, sweetie pie, dearest, my infinity
Yours: mama bear, cuddly cutie, majesty

Mirio

His: peek-a-boo, boo bear, muscle man, smiles
Yours: flawless, dove, his miracle