surprised pikachu

You are partly right.

In short: The muscles use ATP to make energy, that reaction takes oxygen. When you’re not able to provide enough oxygen for the amount of atp that you want to convert into enrgy your body starts producing lactic acid which ends up in your stomac and you puke.

This is the same thing that happens when you run so much or so fast that you vomit. It means that you are pushing your muscles harder than your lungs can keep up with.

For a full accurate read check out this https://strengthmatters.com/anaerobic-lactic-energy-system/