Depo shots

I’m about 6 weeks late for my depo shot. Ive been brown spotting for about 2 weeks now on and off. So i went today to get my shot. My pregnancy test came back negative and they still told me i need to wait 10 more days to get my shot. How possible is it to get pregnant in those 10 days? I do NOT want another baby ( i have a 2 year old and a 8 month old already). Any depo stories? My first son was a depo baby. But it took me about 2 months of missing it to conceive him.