Today I'm pregnant 8 weeks & 4 days, my doctor said I gotten pregnant 6 weeks ago but on the third of July I was already 5 weeks and I did not have a menstrual cycle at the end of may, so did she get my days wrong?

Do two weeks matter at this point in your pregnancy? Unless you know the exact day you got pregnant (and no woman does), the age of the pregnancy can vary by two weeks one way or the other.

Are you concerned about who might be the father?

No I am not concerned about knowing who the father is, the days and the due date all matched up from when the doctor told me I was pregnant I'm just wondering why this doctor told me I got pregnant 6 weeks ago when I did not bleed the end of May as well as the end of June.

The due date is putting me back at May the 28 that's when I most likely gotten pregnant. This is my first pregnancy I don't want my doctor to confuse me I was told multiple times that she's way was off and to get better information ( second opinion) from a different doctor.

You don't need a different doctor over something like the due date/how pregnant you are. You haven't even told us when your LMP was. It's all guessing this early anyway.

Calculate your own:
Due Date Calculator: Calculate Pregnancy Due Date (http://www.justmommies.com/duedate.shtml)