a positive is a positive! congratulations! and stop worrying - your dr probably wants to give you more in depth advise than just say yes or no over the phone. Sometimes dr's don't really understand how a 24hr can wreak havoc on our minds.
She will prob want to do standard test like check your immunity (rubella/chickenpox), advise on taking folic acid etc. and do blood tests to confirm preg officially.

Congratulations again and I think you should celebrate hun. Goodluck telling your folks.