It's unlikely that you are having a miscarriage--but possible. You should not read an HPT before the time limit because of the likelihood of an error like you saw. With a period 6 days late I'd expect that the test would be strongly positive. A positive test will stay positive and generally get stronger throughout the testing window. Likewise, a negative test can sometimes show a faint positive after the time limit. I've had that happen several times. That said, if you are having pain in one side only, you could have an ovarian cyst or a ruptured cyst (not serious, very common, I've had several though they are very painful) and generally do not require medical intervention.
The brown blood means the blood is older and has been sitting around longer consistent with the late period. Nothing else sounds too alarming.
Years of infertility but regular perios, LOTS of contact with OBs and infertility doctors, tons of pregnancy tests and late periods and 3 miscarriages have taught me more than I ever wanted to know about PG tests, bleeding, missed periods and wishful thinking.
If you are in severe pain, see your doctor. Otherwise, it's probably just a bad period.
Also, if it is a very early MC, you don't need to do anything about it. You body is doing its job.
Good luck!