A new mattress is no guarantee of improvement, unfortunately - been there, done that. You probably know this already, but you will need to address the cause of the back pain itself. You may already be doing this, of course..
Sound advice.
I go to my phisio to correct anything that can be first.
Having worked in a heavy back breaking industry for over 30 yrs I've suffered with 2 main issues.
Neck and lower back.
Now a firm bed causes my neck to play up. Soft causes my back to ache
The best mattress ivehad was a firm mattress with a built in memory topper.
By far the best, my new mattress is ok but i cant wait too change it.
Wife likes it but it's not working for me.
Other and possibly as important is your pillows.
Getting that right is half the battle.
Too firm i hear my pulse in my ears.. Too soft iget neck pain.
Bit like hotel beds, I've stayed in top london Hotels and various expensive places and suffered a terrible nights sleep, but the best sleep ive had was a Premier in in St Austell on the way to Cornwall this summer, perfect, i could happily steel the mattress
if i could get it in my bag...
Good luck,