Last Wk Negative. This Wk Positive. 6Wks?

Ellie • 💙 1-28-16
So I went to the dr. yesterday and found out I am six weeks and due Jan. 20th. My concern is I am not as far along as they think. My missed period was May 18th. I tested on the 20th in the morning and got negative result. I waited almost a week and tested again and got positive. Is it normal to be 6 weeks and to have had a negative test last week?