How can i prove back pain to disability doctor?

Not possible: Pain is subjective and no one can prove that you do or don't have it. For disability ratings, pain doesn't factor into it heavily. The doctor can only go on things that are considered objective and reproducible. They may have sympathy for your pain but the rating scales don't allow that to be rated heavily. Pursue strategies for pain control and try to be as mobile as possible.

Doesn't matter: Pain of any cause or any severity by itself isn't a medically definable impairment. You have to have other conditions that combine with it to equal a disability listing, or you have to establish that your residual functional capacity is low enough to qualify on that basis; with pain alone, that just doesn't happen. Ever.