Umm welcome to lesson barns? Saddle fitting issues can be helped with proper padding, but more importantly it shoud fit you as best it can rather than the horse. Trainers don't have one saddle for every horse, they usually have one and pad accordingly. Some horses with saddle issues can be ridden in the horses owners saddle if it is fitted to them and fits the trainer well. Saddle fit can be a problem for horses, and there are certain trees that are better for multiple horses, but they are expensive and aren't really intended to be just for one horse, unless the horse really demands a custom fitted saddle.
Troubled TB ~"A thorn by any other name will prick just as deep." @-'--,---