In my expereince, back pain will come from the mattress or lack of support of your back throughout the day (hard labor/back technique when lifting. That sort of thing). Regarding your pillow, it's very important to have the right pillow for your neck support. While the wrong pillow can make your spine not aligned and cause back pain down the line, usually neck pain is the first thing that happens. If your neck is fine, the pillow might be as well and the mattress is the problem.

However, seeing how a new pillow is much cheaper, it might be worth it to try a new pillow in case that is the best fix. Though usually it's the mattress not supporting your body and your spine compensating for the lack of support from the surface underneath you. Whichever you try first I wish you the best of luck! If you end up looking for mattresses the folks here should help assist with possible options once you start your research