I had unprotected sex 21 days ago 11/26 is it possible to have positive pregnsncy test and spotting last period was 11/13-18 or did i conceive earlier?

Both possible: If your last period 11/13/13 was normal, then 11/26 would have been within a few days of your most fertile time. So if no period and positive pregnancy test now, most likely you just conceived, but possible you conceived earlier. An early ultrasound will confirm how far along your are and from that can know about when conception occurred.