Pregnancy test

If I had unprotected sex (not intentional - condom bust!!) on 26th December, would a pregnancy test show positive by now if i were to be pregnant? That’s 3 weeks so I would think if I were I would see it on a test now - the one I took this morning was negative.

I’m 12w post partum, breastfeeding and haven’t had a period yet so I feel all over the place at the moment. I had very slight bleeding just before NYE that I worried may have been implantation bleeding and a little bit of cramping last few days.

I didn’t find out with my first until almost 9 weeks as I have PCOS and a lot of my symptoms and missing period clashed with that so it wasn’t until I took a test to rule it out I found out I was pregnant