No - it's biologically impossible to get pregnant during menstruating.
Yes - you can get pregnant as a result of sex during menstruation.
During menstruation there is no egg present for sperm to fertilise and the uterus lining is shedding so a fertilised egg wouldn't be able to implant, however it is possible to be fertile during your period if you ovulate early in your cycle and there is fertile quality cervical mucus present which can keep sperm alive in your vagina for up to 7 days, by which time you may have ovulated.
During a 24 day cycle you'd ovulate roughly on day 10 of your cycle, that would mean potentially you'd be fertile from day 3 of your cycle - also remember that you cannot judge your current cycle by past cycles, your average cycle may be 24 days but this cycle may have just been 20 days, and thus when you had sex you were probably fertile...so pregnancy would be a possibility.
It's really important that if you're going to have sex you learn how conception occurs, also if you don't want to fall pregnant it's important you use birth control methods and emergency contraception when it's needed. Your period may just be late, but if worried get a pregnancy test.