Short answer: Yes, the fast remains valid if you only vomited and did not intentionally consume anything.

Details (simple and practical)

• Vomiting itself does not break a fast in Jain maryada. It is an expulsion, not an intake.
• After vomiting, rinse your mouth well and spit. Do not swallow anything back.
• Do not drink water at night. If your fast is tivihaar/nirjal, even daytime water is not allowed; if it is upvaas with boiled water, that is only by day, not at night.
• If you accidentally swallowed some vomit or drank/took anything by mouth at night, the fast is considered broken.

Health exception

• If there is a genuine medical need (severe weakness, dehydration, medicine required), protecting life takes priority. Give up the vow respectfully, take what is needed, and do pratikraman. Next morning, perform proper pārṇā (breaking the fast) as per time, and take a new small pachchhakkhān.

Notes by tradition

• Shwetambar and Digambar both treat involuntary vomiting as not breaking the fast, provided there is no intentional intake afterward. Night-intake would break the fast in both traditions.

For simple guidance on parna timing and method:

• Parna timing and care:
• How to break a fast gently:
• Types and rules of upvaas (including tivihaar):