Could a pinched nerve cause lower back pain?

Absolutely: All the nerves that travel down your leg originate from your back, and a pinched nerve commonly causes low back pain.

Yes: The goal is to relieve the pressure on the nerve a diminish the local inflammation. Resting in a position to relieve strain in that area is useful. Icing can be a great relief and the use of nsaids is frequently helpful. Massage is a good reliever but if the condition persists week after week or is worsening, then you need to be evaluated by your orthopod.