I agree with the people above, if you have any hunch your horse has a sore back, get a professional out to evaluate. That can be a vet, chiro, physiotherapist or good certified saddle fitter.. The saddle fitter I'd recommend anyway, as the leading cause for a sore back is an ill-fitting saddle.
Some things for you to help with gauging whether the horse has a sore back: grab a stool, stand next to his back and gently but firmly push your fingers into the muscles next to the spine (the longissimus dorsi, if you don't know where those are, google it), start at the whithers and move them back bit by bit. If the horse shows any reaction any way, biting, lifting a foot, even swishing their head around, swishing their tail or tensing the muscles under your hand like they are pulling them away (some even completely arch their back, it hurts so much) and they do it consistently when you push there, it's very, very likely they have a sore back, which will most likely be either from the saddle or from lameness that has caused the horse to carry himself differently. Also put the saddle on the back without any pads (if western saddle, you do put the pad under it) and check whether it is touching the spine anywhere, this could also lead to a sore back. Generally just feel the back for bumps or other irregularities, hotter spots than the skin around it, and the tension of the back muscles. Any of these being there could be an issue, or point to backpain.