Possible miscarriage at 6 weeks?

I just had my son in May of this year. Exactly 6 weeks later at my PP appointment I was cleared for sex and also started on the birth control patch. That night hubs and I had unprotected sex. He pulled out but I know there’s a possibility of getting pregnant still, and that you’re incredibly fertile after giving birth.

6 weeks later (12 weeks postpartum) and I just started what I think is my first period postpartum. It seemed a little later than what I thought it would be considering I’m not breastfeeding, which I know can prolong time without starting your cycle. I’ve only had some cramping daily and very light pink spotting with some clear discharge for the past 3 days. Figured it was because of my birth control patch. Today while at work I went to the bathroom to change my liner and I had what looked to be a clot on it. But it had some firm creamy discharge looking spots in it. I used a piece of toilet paper to pick it up and it wasn’t slimy or very wet just firm and thick. I didn’t have my phone so I couldn’t take a picture. Could I have actually been pregnant again and had a miscarriage? What would one look like this early on? Would a pregnancy test still show up positive if I took it now?