no, that isn't possible.
your baby was born almost on his/her due date.
a dating scan which measures the gestation very accurately (but allow a day either way) put your due date at dec 30.
so while your periods might be irregular and your april spotting/bleeding may not have been a proper period, you almost certainly were not at that point already pregnant.
to be due on dec 30 and have a full term baby on dec 31 means conception is most likely to have been april 8/9.
that means any sex you had between 4/5 and 8/9 is what got you pregnant.
if you are 100% sure you didn't have sex until april 10 then that is probably when you got pregnant (allowing for a day out here and allowing for a day either way on a dating scan).