Breastfeeding and birth control

I exclusively breastfeed my 3 month old but she doesn’t eat in the middle of the night ( she eats at 11:30 pm then sleep until 9am ). I thought i had gotten one period but it was very light ( mostly only blood when i peed barely enough to cover a pad and no cramps really ) then didn’t get one again. I really don’t want to be on birth control but i really don’t want another baby so when we have sex we use a condom and he pulls out.. would breastfeeding also be a back up birth control method ? I’ve heard it works in most cases if you are only breastfeeding which i am but i don’t know if the fact that she doesn’t breastfeed the 2-3 hours at night make a difference . also is it strange i didn’t get a period again? I THINK that one was a period but looking at it maybe it was just still light spotting it was at 7 week pp