I missed one active pill and has unprotected sex that night. The next morning when I went to take my next pill, I then realized I missed it.

I called an OBGYN and she said take both pills and I should have breakthrough bleeding and make sure sex is protected for the next 9 days.

I am concerned because I had no bleeding and I am nearing the end of my pack.

Is it still possible I am pregnant?
And when should be the best time to do a home pregnancy test?

Yes it is possible that you are pregnant. Even used perfectly, birth control is not 100% effective, and human error decreases the effectiveness. Take a pregnancy test at least one week after you miss a period.