You're not likely to conceive having sex a day before your period, you'd be at your lowest fertility.
Ideally, you'd have sex just before you ovulate, normally between days 11 and 16 of your cycle. Day 1 is when your period starts.
Sperm can survive about 5 days, the egg, only 48 hours after ovulation.
What you saw is not specific to pregnancy. It may be just old blood.