Almost everyone has an imbalance in leg length, most other limbs and even facial features. So it is not surprising if the doc says this to many people. The issue is not the difference, but in how our bodies adapt (or not) and often in whether something changes in later life due to injury, arthritis, or joint replacement.

My legs are quite different in length, but my body had adapted. In my 40's I had a knee injury and repair surgery and the difference increased, leading to additional stress on back and hip. Again, my body adapted.
20 years later, while replacing my hip for the 3rd time, my ortho decided to try to even things out - wow the pain while recovering - the PT put me through gait training, completely reteaching my body how to move. Now, 10 years later, it still gets achy sometimes, and if I stand in bad shoes or barefoot, my back and leg hurt for days and nights.

So my recommendation is for a thorough PT evaluation by a rehab specialist, who can tell from positioning and evaluating you both lying down and walking whether there are things you can do to help.

And proper orthotics, or even lifts or a built up shoe can be a permanent answer. This should be done by a trained orthoticist or podiatrist, using the diagnosis from both PT and ortho.

I still have spinal stenosis and arthritis, and leg length difference. But if I sit and move right and wear good shoes the pain is manageable.
Sue

Your pelvis may need realignment. A good physical therapist can check for that issue and correct it, so that one leg no longer appears to be longer than the other. Perhaps that issue is causing the back pain.