I'm a little unclear of exactly what happened here, but if you forgot sugar pills, you're absolutely fine. You don't have to take the sugar pills--they're just there so you stay in the habit of taking a pill every day. So if you missed some but started the next pack on time, you're good to go.
A blood test is more accurate than a urine test, and I believe the first response brand urine test can detect up to a week before a missed period, although I'd give it a bit longer to make sure. Most birth control pills only advocate taking a pregnancy test after your second missed period, since it can happen occasionally (and if you just finished your first pack, things might have been a bit weird, causing you to not menstruate).
I don't know exactly when a transvaginal ultrasound would be able to detect a fetus.
Also just as an fyi when I input my lmp (6/1/13) I get an estimate of approx 6-7wks pregnant but that isn't possible as I was on b/c and no intercourse. When I input what should have been my lmp (07/01/13) give or take I get 2-3 weeks pregnant which makes more sense as that's about when I had intercourse. Would an hpt pick up a positive hcg level? Would a transvaginal pick that up?