Quoting Scared & Excited:" The baby was actually 13 weeks."
If you were due in mid april, you'd have been around 16-17 weeks now (i'm 6 weeks behind that roughly and I'm 10 weeks)--and you miscarried two months ago, so subtract about 8 weeks. That leaves 8-9 weeks. Doesn't add up to 13 weeks like you say. was your due date off?
Either way, even with a 13 week loss (I have lots of experience with losses at all kinds of gestation), you'd have lots of symptoms if you had retained placenta/fetus (which would be the only explanation of HCG still being in your system 2 months later). Since you've had a negative HPT since you lost that pregnancy and have what you say are faint lines now, then the only explanation would be a new pregnancy.
As for your current bleeding, if it is light/spotty and not red, it could be implantation issues or your body could be low on progesterone because you implanted late and your body started the shedding process around the time the egg implanted, so your body got mixed signals and needs a little time to sort itself out. Some bleeding CAN be normal in early pregnancy. it never has been for me, but I now many women who have had healthy pregnancies after having early bleeding. Could be a subchorionic hemorrhage (a bruise in the uterine lining), or a pool of blood from implantation making its way out finally, or it could be a low lying placenta near your cervix being irritated by you moving around, it could be a lot of things. Only time will tell if the test gets darker or if you get a blood test and hour HCG is doubling properly---I'd call your doc when you can and ask about a blood test to ease your mind since you've had a later first-trimester loss previously.