Hi,
It sounds like what you had was a chemical pregnancy. Your last normal period was the first week of Nov, you should have had another the first week of Dec. but instead bled around the 16th after a positive test.
If you look up chemical pregnancy it should help to explain what happened. Basically the embryo didn't implant correctly or was so nonviable that the body rejected it immediately. In this case it is not unusual to only bleed for 7 days and not have a lot of tissue. 3 false positives are rare so for a couple days, yes your body was producing pregnancy hormones. Most women have had a chemical pregnancy and never knew it. The classic sign is a 1-2 week late period. Another is a home pregnancy test positive that can't be confirmed by the doctor. The hormones are only in your system for a couple days so it can be hard to verify.
As to your next period.... I'm fairly sure I went through this last January but I never tested. My cycle dates were then off a little for a couple months. Your body may wait until the first week of Feb to have a cycle again as it depends on when you next ovulate. I suspect that you will get it sometime in the next week. If you don't I'd call your doc to see if they are concerned, if not just wait it out until Feb.
I'm not sure if you are currently trying to conceive. If you are, there is a slim chance that your next cycle is late as you have already conceived again. Very rare, but possible. You might consider taking another hpt to verify this. You also might consider waiting though to avoid another "false positive".
Good luck and I hope everything turns out alright. I'm sorry for your loss. It's one of the reasons people are recommended to test the week after their period. It wouldn't have helped in your case but most chemical pregs are lost immediately and just show as a late period thus causing no emotional stress. Your post seems to be more concerned with moving on which is good.