The spotting may just be implantation. For some reason in both 2 of my pregnancy I had spotting really early like 6 7 weeks in doctor said it was implantation and I had a positive test like yours and just kept getting stronger. Bleeding did stop and currently 26 weeks with baby 2
I’ve talked to my nurse about this when I found out I was pregnant also and she said it’s very rare to have a false positive on a pregnancy test however it can happen.