I want to know the exact day the I came out pregnant my last period was October 16,2010

It is impossible to give you an exact date. It's pretty much a well educated guess.

Why is the specific date important? Is there a question about who the father is? (I see this question on the legal boards.)

If your LMP was 10/16, it's quite possible you got pregnant on 10/31. Now, please understand that this is not an exact date, only an estimation since it is impossible to know exactly when the sperm met the egg.

In the end, you will have to have a DNA test to determine paternity.