It's entirely possible, but read over this quick-guide for obvious pregnancy signs/symptoms posted by a fellow member and obstetrical nurse, J_9; it's very informative .
https://www.askmehelpdesk.com/womens...ant-78869.html
Regarding periods, yes it's entirely possible that you can still be pregnant if you are bleeding. It's fairly normal early on in pregnancy. Let this period run its course, then take a test with your first morning's urination afterwards. If it's negative then you're probably okay BUT there are always exceptions. If you don't get your period next month then take another test. If you're freaking out about it that much, then go see an OB/GYN.
Our bodies can be very finnicky with hormones. Sometimes you might miss a period and/or get it late for no reason other than exercising more or getting stressed out. If you're menstruating now you SHOULD be okay, but in the future DO remember to use condoms and maintain a proper course of birth control, such as the birth control pill.