Positive at 3 weeks?

Sorry if this seems completely crazy but I’m so confused.

So I had an early miscarriage last month, I was no more than 5 weeks (but can’t be sure because I never even got the chance to see a doctor it happened so quick). A few days after the bleeding stopped I did a test and it was stark negative. I did a few test (all different brands and types) and all came back negative so obviously safe to assume miscarriage. This was 4 weeks ago now. Crazy thing is over the past few days I’ve have very obvious and bright positive tests including a positive digital (again all different brands and types). Going off my miscarriage I should of been 3w3d when I got my first positive and I’ve just read it’s not possible to get a positive (let alone a strong one) that early. Is this true or is there any explanation for this? It crossed my mind that maybe I didn’t miscarry but the multiple negatives and heavy bleeding would suggest I did. I have to wait 3 weeks for a scan because they’re completely booked out and can’t get my bloods done for another week and a half for the same reason. I’m going mad over here! Anyone experience something even remotely similar or maybe have some insight? I can’t stop testing because I’m so scared it’ll go away but I’m going broke buying tests lol