Within about 10 days or so BEFORE your period the odds of pregnancy are decreasing, so it is less likely you'd get pregnant.
Normally you'd ovulate between days 11 and 16 of your cycle. Day 1 is when your period starts. 48 hours after ovulation the egg is not viable and you're not likely to get pregnant (day 18). Since the normal cycle is about 28 days you have about 10 days at the end where pregnancy is unlikely.
Preejaculation fluids, precum, can contain sperm especially if he has recently (since his last urination) ejaculated.
In this case I don't think you need to worry about pregnancy.