You can generally start BC pills on any day that you want and it doesn't have to be the first day of your period. Thats just suggested because while you are on your period, you're not likely to be ovulating and so you are protected sooner from pregnancy(after 7 days I believe). And sometimes people spot if they start it at a random point in the month since the body goes "woah hormones! must do something!" But it gets straightened out after the first month.

The general rule for pregnancy protection is at least 21 days of active pills and no more than 7 days without. You can have more than 21 days of active pills(ex: skipping a withdrawl bleed), but just make sure to not go more than 7 days without.

you could always see if theres a online pharmacy or mail-order pharmacy that has the prescription available, then have your doctor fax in the prescription.

someone correct me if I'm wrong...I'm a bit tired(ugh finals!) and my brain may be overworked.