I had sex and the condom broke, the next day i started my period. It wasn't as heavy as it usually is. I know sperm can live inside you for up to a week. Is it possible for me to be, or become pregnant still?
It's very unlikely you will get pregnant.
You are at your lowest fertility just before your period. The egg is not viable. Sperm can only live about 5 days and you won't ovulate until about day 11 of your cycle (12 days from when you had sex).
Don't worry about it.