@Empanada: Stamp with your feet on the floor during a tantrum can be "patalear".
Se puso a patalear porque no le compraron el juguete.
He/she started to stamp his/her feet on the floor because they didn't buy him/her that toy.
Hizo berrinche porque no le compraron el juguete.
He/she threw a tantrum because they didn't buy him/her the toy.
As for "chillar" as a synonym of "lloriquear", I tried to make clear it's a Mexican usage. It's a pejorative way of saying "llorar". Can be applied to adults and children equally. It's used to express that it's (more than) bothersome the way they behave.
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