Backaches are often caused by wearing bras that aren’t supportive enough/bras that don’t lift.
First, make sure you are wearing the correct band size. In order to lift your breasts, the bra band has to be somewhat snug. Try putting two fingers between the hooks and your back. If you can fit a whole hand in there, size down in the band.
Second, try bras with wider/stronger bands, and thicker/less stretchy shoulder straps. The spandex content of a supportive bra band should hit at least 15% (the fabric component that defines how much it stretches, and how much it ‘recovers’ from being stretched).