Physical therapists are trained to handle a wide range of musculoskeletal problems. Their particular expertise is with the human movement system. That means they look at the whole person, not just one moving part that’s having problems on any given day.
But it is true, that once trained and out in the field, some therapists do specialize in a particular problem or body part. When it comes to back pain, there are several different ways therapists approach the problem. Manual therapists (those trained to do joint mobilization and manipulation) are more highly skilled at treating back pain problems compared to a general practitioner.
But a good general practitioner can get you started. And if you need more specialized treatment than they can offer, they will make a referral. Since the therapist is most likely to know where to send you (if even needed), the process is more streamlined than trying to figure out for yourself where to go or who to see.
Give your therapist a call and ask this question directly. It will answer your question and may save you time in the long run.