Could having protected sex 3 days before my period cause my period to come late?

No: Your period starts about 14 days after you ovulate (unless you get pregnant). Once you ovulate I know of no factors (other than pregnancy) that alters this. Various factors can influence when you ovulate, so if your period is late (and if you are not pregnant) then you ovulated later than usual. It is not unusual to have late periods now and then.