Hi there.
A pregnancy test is quite accurate, and I believe that this positive result should be investigated further.
You may indeed be pregnant and these bleeding may be due to some form of miscarriage or ectopic pregnancy.
The bleeding may also be explained by implantation of the fertilized egg within the endometrial lining and
cause some bleeding. Abnormal pregnancies such as molar pregnancies may also explain this phenomenon.
I suggest you return to your gynecologist to have this evaluated. Regards and God bless.