Postpartum sex and pregancy

How long after delivery can you do a pregnancy test. I know a lot of people say you are extremely fertile after delivery and shouldn't have sex until six weeks. Just want to know how long hcg stays in your system after having baby? I'm six weeks postpartum and did have intercourse and had a positive blue dye early detection test this morning? Negative pink dye test and negative digital, we did use an unreliable method of prevention so I just want to know how reliable tests are at this stage?