Is it possible to be pregnant when missing a pill on week 1 and vomiting on Sun of week 3 and having negative urine test next day and getting period on week 3 of active pills start new pack on Sunday?

Because you got your period its unlikely you're pregnant. Based on what you said, it sounds like the Birth Control pills are not acceptable for you and are causing these symptoms. You need to see your doctor about going on a different birth control. If you dont you will put yourself at risk of pregnancy.