Well, given that your period is now over a month late (it should have come at the end of January, right?), if it was late because of pregnancy your hormone levels should be high enough at this point to get a positive test result with or without "first morning urine."
Urine tests at the doctors office actually IS pretty standard. It's less invasive and faster than blood tests, so it's kind of the go-to test. Your doctor can ORDER you a blood test if things are inconclusive.
I doubt you're pregnant. Tender breasts and nausea are symptoms of just about EVERY hormonally weird things, including pregnancy but also weird changes to your normal cycle (which seems like what you're dealing with).