I'm just curious, but why do you need to know the conception date so badly?
Your son was not "supposed" to be born on the 20th. The 20th was his
estimated due date. It is normal for a child to be born 2 weeks before or after this date. And since you were given an estimated due date, the doctors should have based this either off the first day of your last menstrual period or the baby's size via ultrasound. Either way, they should have given you an estimated conception date.
I hope this helps.