Cracked ribs, broken ribs, thorn in flesh that saddle is hitting or girth is.
Saddle could have broken tree, nail/screw/something has worked loose and is jabbing her, or even have something in blanket too.
You need to stop riding the horse if this is happening. You are doing something that is causing pain by continuing to ride her, this is not your horse, and if you don't have the money to have a vet out, and also get the owner's permission too, then this is wrong to do to the horse.
I've seen bad farriers, poor trimming and I've never seen one cause a horse to rear under saddle. This is something else.
Leave the horse alone until this is addressed.
Horses make me a better person.