Possibly, take a test AT the hospital, theres tends to be a bit more accurate than one from like walgreens/walmart. If your not that worried then go to walmart and pic up a test and check. Just because your late doesn't mean your pregnant though.
Yes, you could be pregnant. I think the at home pregnancy tests say that you're suppose to take them a week after you miss your period so looks like you can spend the money you saved on condoms on a pregnancy test.