Could this be a chemical pregnancy like the DOC said?

How long can a chemical pregnancy cause a positive in a PT for? My last period was Feb 28 and I had an ultrasound done at 6w and the doctor at the hospital didn’t see no baby (didn’t mention me if he seen a sac or not) “he didn’t see anything. I had an ultrasound and a vaginal ultrasound done too. I should be 9w3d today and I’ve been taking pregnancy test and they’re still showing up positive...... I haven’t had not one negative and it’s been 3w since I last seen that doctor. I’ve had very mild nausea and sore breasts. I still have milky discharge too.... I’m so confused. Not sure if these lines are dark enough.. also, I haven’t bleed either