Usually when you breast feed, you don't ovulate. But, anything is possible.
Yes because you ovulate before your period arrives so you may not have got your first period yet but that could be because you've fertilised the egg that would caused that first period had you become pregnant. It isn't all that common as breastfeeding suppresses ovulation in a lot of women but it not extremely rare either.
Had you not become pregnant** sorry
My sister got pregnant with her 3rd child while she was breastfeeding her 2nd (about 8 Mos old). She found out when she went to the Dr to go on birth control. So yes. There is a birth control pill that is safe while breastfeeding if you do not want to use condoms.
I was breastfeeding and taking the mini pill when I got pregnant with my second. You should test