Generally, no.
Every vagina is different. Most girls will experience a natural disintegration of their hymen by their mid-teens, so a doctor wouldn't necessarily be able to tell if you'd had sex.
However, it's a good idea to tell your doctor - the more information they have about you, the better they can offer advice and support. Before you tell him/her, be sure to ask what their policy on confidentiality is.
If you know you can talk without it getting back to your parents, then you can feel free to discuss sex-related issues, birth control, etc.