If you had your period and it wasn't severely light or anything on that side of abnormal, you're not pregnant. But yes, pregnancy tests can be wrong sometimes. In this case, I doubt it is since you say you had your period.
Yes, pregnancy tests can be wrong, especially home ones if you didn't follow the directions exactly. Blood tests are more accurate.
Although it's unlikely, yes you can have your period while pregnant. One of mother's coworkers had her period, which was only a day shorter than normal, the whole time she was pregnant (it actually took her until she was 7 months pregnant to find out, because she was in denial/still had her period, and was large enough not to show).
If you're worried, you should talk to your ob/gyn and get a blood test. In the mean time, you can act like your pregnant and avoid smoking and drinking, and make sure you're eating a healthy diet. Those measures won't hurt you, and on the off chance you are pregnant, your baby will be off to a better start.
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