is it possible?

I have a 9 month old, still exclusively breast feeding, still no period but I took an ovulation test this morning and it is super positive. We had unprotected sex Saturday, how likely is it that a sperm would live in there until now?! Really not wanting to get pregnant so soon. Sex with condoms had been hurting so badly after I had the baby, the IUD they put in tore inside and had to come out and they won't put me on a bcp. I thought we were okay since my period hasn't shown any signs of coming back. I'm not sure what to do, but I'm so anxious about it.