(TW-Vomit) Should vomiting let you stay home with no signs

So hi before i get into the story/rant i have some context my mum is not a strict mum but doesnt let me stay home if i feel sick anymore because she said that have to vomit now to the story. so last friday i woke up and found out that i go 2 hours later to school beacuse pe was cancelled so i had time to eat breakfast and after eating the breakfast like 20 mins after i felt that i needed to throw up so i threw up in the toilet and told my mum on phone and she said that im still going beacuse there are no signs that i was sick before even tho I was sick on thursday and told me to go to school and then i vomited once in school i need some peoples opinions beacuse I dont know how to feel about this