Allergic to latex and animal hair, need a mattress for a bad back

We are looking for a new bed or mattress, we currently have a 10 year old firm mattress and slatted base (king size) heights 5.10 and 14st, 5.3 and 17st. We are both experiencing backache. We had a great night sleep on a Novotel bed recently, but wondering what you would suggest. I think we would be more comfortable on a divan base with a medium to firm mattress with a pillow top. Allergic to both latex and animal hair. Thanks in advance for advice.