The only thing that would cause bleeding from the swap is if you put the swap too far in.
It should only go just inside the vagina, around the anus and the perineum - like only the depth of the cotton tip itself.
Provided you did the test correctly, the spotting is most likely unrelated to the test.
It is possible you have small hemorrhoids...although at your stage of pregnancy I wouldn't be surprised if you have some spotting from your plug. I was spotting for on and off over about 3 weeks from 35 weeks, had a small show at 37 weeks.

Anyway, Im sure you are fine. If the bleeding increases markedly, see your doctor.