My experience was similar. I understand how scary this is. My hpt was positive, my blood test was positive, I had a little bleeding that wasn't bright red, and they couldn't see the baby on an ultrasound at six weeks. Mine turned out to be an ectopic pregnancy.
Yours could be something different, but ectopics are life threatening to you. Don't let fear keep you from going to your appointment. I recommend you call your doctor now and tell him about the blood so he can decide if you need to come in sooner.
Hopefully it is something along the lines of you ovulating late and the little bit of blood is normal, and your baby will show up on an ultrasound soon. Just be careful and if your bleeding gets heavier, see your doctor asap, or go to the emergency room if needed.
Let me know how things go for you today.