Ok, so I had sex on the second day of my period and my flow has kind of stopped, but the guy didn't ejaculate inside me. Should I worry??

Not ejaculating inside the woman is the least effective form of birth control.

There is another thread on this same subject. Yes, apparently you CAN get pregnant during your period. It thought the chances were slim but apparently they are not.

https://www.askmehelpdesk.com/pregnancy-new-motherhood/condom-broke-same-morning-got-period-680817.html

I'm not a medical professional, so this isn't a medical answer just one of personal experience, but whenever I have sex during my period it stops it for a little bit. But Judy is right, you can get pregnant during your period. That's why you ALWAYS need to use protection, along with the risk of STDs.