Are you sure you've had warts for 11 years, or is it possible that your first wart outbreak was due to one strain of the virus that you perhaps caught from one person, and the second bout (your current one) came from someone else? Have you had warts consistently for 11 years, or have you just had two outbreaks 11 years apart? If it's the latter, than it's almost definite that you have not had warts for 11 years, but have had two different strains of HPV.
Also, to respond to your question- unfortunately, embarrassment shouldn't come into play when you see your doctor. Your doctor has seen everything you may show him/her and probably much worse. My advice to you would be to understand that doctors study these sorts of things, and are trained to deal with them, so there is no reason to be embarrassed. You should see your doctor and have them treated (if, they are, in fact warts).
It is strange you say you have had them for 11 years? They usually clear themselves within 2 years and after that period is often rare to occur again in the future so have you had your warts for 11 years? If so i would say that they are not warts