I bought a hard (4) matress last year. Because a doctor said the harder the better. Now, I have low-key backpain, can't recommend.
Never had any back pains.
And my father's doctor agrees with your doctor, and I have had this kind of bed since my early childhood.
I have trouble sleeping in soft beds of hotels and other places.
I do stretching, running, or swimming- one or multiple of these all year.
I guess that is what saves me from back pains and other trouble despite bad postures.
Even when I didn't exercise (before age 14), I did not have any back pains despite sleeping on a very hard mattress.
Talk to your doctor and/or do a little exercise regularly. That should help. Don't start exercising with existing back pain without consulting an expert, though.
So, yeah, I'll do more training.