As above get a diagnosis of the back problem, you do not say where the pain is.,…is neck, between shoulders, lower back….check out what it is.
Then look at mobilisation this could be anything from physio, osteopath or chiropractic – everyone has some type of practitioner they like best personally osteopath and I would never ever use a chiropractic again.
Get into a routine of stretches for the body and back. Look at developing core muscles and hip flexors plus losing IT bands down your legs. This may alleviate the problem.
Bike wise yes full size does stop some of the battering bit, fit and sizing is really important, but a good steel hardtail with a suspension post (use or thudbuster) or a carbon post may also work.
If you go for a full suss then 29er 100mm travel with 120 mm fork is a hugely capable bikes,
Rocky Mtn element, wonderful bike owned one
Anthem, owned in 26 flavour
Specialised epic or camber { more travel}
Santa Cruz super light
Good luck