My question is that does vomiting break your fast?

If you had not vomited intentionally then your fast is valid and don’t do anything from now which can invalidate your fast. Please see the Fatwa of Ayatullah Sistani ( May Allah protect him)

Whenever a fasting person intentionally vomits, his fast becomes invalid even if he vomited out of necessity or because of illness or suchlike. However, if he vomits unintentionally or involuntarily, there is no problem [and his fast remains valid].

Ruling 1617. If at night one eats something that he knows will cause him to vomit unintentionally during the day, his fast is valid.