The recommendations for cervical cancer screenings differ significantly based on where you live. The North American protocol of annual screenings as soon as you've had vaginal intercourse, or after a certain age even if you haven't depending on where you are, will result in the average woman having 40-50 tests over her lifetime or so, depending on when they start and stop, and a 95% chance of a biopsy or something frozen/cut/burned off, yet if untreated, only a 1% risk of cervical cancer in the highest risk groups (unprotected sex with multiple partners). In Finland and the Netherlands, even the highest risk groups don't get tested until they're 30 (false positives are *far* more likely the younger a woman is, normal cellular changes are read as abnormalities), and then every 5 years afterwards, for a total of 5 to 7 lifetime tests, and in the UK apparently they can't force you to get the test - they need to tell you about the risks of false positives and how unreliable the screening actually is, now.
If you're under 30 and consider yourself less high-risk sexually than the average denizen of Amsterdam's red light districts, you may wish to do further research on the topic before deciding one way or the other. It's your body, not the American medical establishment's, or the board's, or or your mom's, or your friends who want you to share their misery.
If you want the vaccine, and are over 26, if you're not trying to get insurance coverage for it, why would a doctor have a problem giving it to you, given that they routinely write antibiotic prescriptions for colds merely to calm an overly-paranoid population? If you haven't been around anywhere near as much as the average 26 year old, and you explain that to your doctor, you'd expect them to want to hurry up and get you that shot fast before you *do* catch it - like if you'd missed any other vaccinations.