How Long After Finishing One Dose Of Ortho Tricyclen Lo Pills Is Restarting Necessary?

I am currently on the birth control ortho tricyclen lo and my pills (including reminder pills) will be finished on Sat. the 16th. The earliest appointment I can get is Mon. the 18th. When should I start them and how long will I need a back up method? Keep in mind my 2nd anniversary is 2 1/2 weeks after my appointment. Will I still be needing back up then?