Doctor gave me lutera w/o a pregnancy test first. my lower back is hurting, nauseous, is this normal?

Totally fine: It's completely fine that your doctor gave you this birth control pill without performing a pregnancy test first. If you are worried you might be pregnant, take a home pregnancy test, they are fast and accurate. If you are pregnant, the pills he gave you will not harm the pregnancy. The symptoms you describe are normal side effects from taking the pill the first few months.