It is usually suggested (depending on who you talk to) waiting 2 - 4 weeks before the pill is effective as the sole birth control method. So you should be fine.
But just remember that if you are ever sick (vomiting or diarrhoea) within 3-4 hours of taking a pill you should class it as a missed pill. And some antibiotics can also affect the efficacy of the pill.
And I guess I should say that there is always the possiblity of getting pregnant even though you are on the pill so be sure you can handle the consequences of this occuring. But I've been relying on the pill alone for a while now and have had no problems