Yes, you can get a positive pregnancy test after giving birth, even if you're not actually pregnant again.
This is because the pregnancy hormone, human chorionic gonadotropin (hCG), can remain in your body for a period of time after childbirth. The reference indicates that hCG can linger for up to four to six weeks following childbirth, miscarriage, or treatment for an ectopic pregnancy. This residual hCG can trigger a positive result on a pregnancy test, even if a new pregnancy hasn't occurred.
Therefore, a positive pregnancy test shortly after giving birth doesn't necessarily mean you are pregnant again. It is often due to the remaining hCG from your recent pregnancy. If you are concerned or unsure, it is always best to consult with your doctor for further evaluation.