It's hard to tell. Sometimes low back pain goes away quickly, and other times it sticks around for months. In people suffering their first bout with low back pain, it often goes away completely within two months, even without treatment. But for some people low back pain becomes a chronic, recurring problem.
There is no way to predict which group you will fall into. The best bet is to get medical attention for your pain. Your doctor can recommend ways to manage your pain, and suggest ways to help you avoid problems in the future. Even if your pain doesn't go away completely, there are many strategies for controlling it so that it doesn't control you.