What can happen if i didn't use a back up birth control plan after being on the new birth control for 2 weeks?

i started getting a breakthrough period and my doctor switch my birth control from desogen to low orgestral i was on the low orgestral for 2 weeks before i had without using a back u birth control method. im still going through the breakthrough period and its been 4 weeks but its not as heavy now. should i have used a back up birth control method