Is it possible for me to get pregnant on pre-cum while on my period?

Not really: if you are truly on your period you are not ovulating and therefore cannot get pregnant. But precum when you are fertile can get you pregnant which is why coitus interuptus is a poor method of birth control with a high failure rate.

Only if you had a: very short menstrual cycle - it is not likely.Most studies have shown low levels of sperm or no sperm in pre-ejaculate with sperm not being motile (however, don't know how promptly samples were examined). One small study published in 2011 showed that there are some individuals with a high motile sperm count in pre-ejaculate. See: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3564677/