Pregnant after miscarriage?

I miscarried in the beginning of November, with Cytotec. I went for an ultrasound that confirmed everything had passed, a week later. I stopped bleeding after a week. The midwives said my pregnancy test came back negative, when I went in the week after thanksgiving. I also took another pregnancy that morning and it too was negative, that I could see.

I got my period exactly a month after I miscarried, it lasted 7-8 days. It ended December 10th. My husband and I had unprotected sex a few times around my projected fertile week, and I’ve since then had a few faint positive tests. Verrrry faint.

Is this from my previous pregnancy, or is it possible it’s a new pregnancy? I’ve been super tired, which I was with my last pregnancy. My period isn’t due until January 3rd! Could the test still be faintly positive from my miscarriage back in November? Or is this a new pregnancy all together, since I got my period?

Thanks!!