If your fast is broken deliberately by vomiting, you must make up the fast after Ramadan, if the vimiting was unintentional, then you don't have to make up the fast.

The fact that you vomit does not invalidate your fast, because if a person vomits unintentionally and without meaning to do so, his fast is still valid. But the one who vomits intentionally has broken his fast. A report narrated by al-Tirmidhi (720) from Abu Hurayrah (may Allaah be pleased with him), that the Prophet (peace and blessings of Allaah be upon him) said:

“The one who cannot help vomiting does not have to make up the fast, but the one who vomits deliberately has to make it up.”