Thanks for the additional information. You can take a home pregnancy test to see if you were pregnant. Tests remain positive for several weeks, even after a miscarriage.

First of all, once you have a period, it takes at least a couple of weeks to ovulate to even have the possibility of conception; then at least another week for a fertilized egg to implant in the lining of the uterus. Since it was only a couple of days between the end of a regular period and the beginning of bleeding again, there was no possibility of a fetus to cause bleeding. There are many reasons for prolonged periods including stress, infection, inflammation, fibroids, ovarian cysts, and many more.

I cannot speak to the impossibility of not having beta hCG high enough to detect until 6 months, since by that time it has reached its zenith, and is declining. The hospital should have its equipment checked. The odds that what you had was a miscarriage are next to nil (and that's giving it the benefit of the doubt). In any event, even if it had been a miscarriage with the slightly longer than normal period, no treatment would have been necessary if it was less than about 6-7 weeks since your previous period.