I'm not sure I would rely on a hpt either - you might still have some hgc left over in your system from the first pregnancy. I would definetly talk to your doctor - don't be embarrassed...i'm sure your doctor has seen or been asked MUCH more embarrassing things, for real. And I am terribly sorry for your loss.
it would be VERY unusual to have ovulated so soon after giving birth
your hormones need to re-regulate even if you aren't breastfeeding (breastfeeding can delay your cycles restarting up to 6-8 months but NOT always)
i can't imagine what you are going through losing your baby, but i don't think you have to worry about being pregnant again this soon.
There is a chance that you could be pregnant already i would definatly do a pregnancy test if you think you are and if it turns out that you are talk to your ob gyn when you go for your appointment