Complex topic. If I understand your situation you were pain free before the new mattress but aren't now. There's a pretty good forum at
The Mattress Underground, and
Mattress Insight with some pinned threads that discuss the best way to audition and select a new mattress. This requires some basic understanding of the different layers in a mattress. I think it's certainly the case that a mattress won't cure back pain, unless it's a poor mattress that caused the pain in the first place. And in those instances, it should be pretty evident either that the mattress is creating hard pressure points, making it uncomfortable to use for a length of time, or provides insufficient support, leading to poor alignment of your back during sleep. According to
Postureg, you may suffer lower back pain due to bad sleeping posture on your mattress.
I don't know the particulars of your new mattress, but at that price point you're probably sleeping on a low-density synthetic foam. That may work well for some people, but there may be longevity issues with the more inexpensive foams.
I keep my mattresses longer than I probably should. The bedding industry likes to cite 8-10 years as a maximum lifetime for mattresses, but I use mine until there's something obviously wrong with them :-) When I purchased a new mattress a few months ago, I was disappointed to find that few manufacturers are making product the way my old mattress was constructed. I auditioned dozens of mattresses all around town and ended up picking up something that is
way more expensive than I expected. So far, I'm liking the new mattress. But I liked my old mattress even more, especially considering the life I received from it and the relatively cheap cost compared to what I have now.
Just know that buying a mattress can be harder than buying a car or a house.