Bougie, the only way to even get a clue in this case is for you to get an ultrasound this week or next, and to tell them you don't know the first day of your last period and would like to get an estimated due date based on the embryo's size and developmental markers. Later in your pregnancy, even an ultrasound will not be very helpful for judging conception dates, since babies grow at different rates. But in the early stages, like right now, with ultrasound input you should be able to assess conception to within a few days. This does not mean go to the ER. Go instead to a good ob-gyn and ask for an ultrasound; if they don't think it is important, explain that you have a dating dilemma. (If they won't do it then, get another ob-gyn.) Even if you have to pay out of pocket, this is your only time window to learn anything, otherwise you will have to wait until the baby is born and do a DNA test. (I suggest a DNA test in the end anyway, but an ultrasound now might help prevent 7 months of worry.)
Honestly, I think timing is so close you are going to have to do a DNA test to determine.