Hello this is Dr. Salama MD,
It does in fact sound like you strained a muscle in your lower back.
This is actually extremely common.
Treatment includes anti-inflammatories, rest and ice
I would take 600mg of Ibuprofen 3 times a day as needed for the pain with food.
You may also benefit from a low dose muscle relaxant prescribed by your doctor.
I also want you to ice the area for 20 minutes, every hour 5 times a day for 1 week.
You may also benefit from the following exercises which I would recommend.
Let me know if you have any other questions.
If not, please don't forget to leave a positive rating as that's the only way I get credit for answering your question.