Yes there is a chance of pregnancy.
Some studies indicate that emergency contraceptives can be effective up to 5 days but the effectiveness diminishes rapidly. Your doctor is correct in not prescribing it.
Where do you live? In the US you don't need a prescription for it over 17 (soon to be 15).
But, you shouldn't be using it more than once per cycle either. It contains a very large dose of hormones. If you plan to be sexually active then use another form of protection either a condom or daily birth control.
Hope it helps.