OP, there are a lot of solutions being offered here by very knowledgeable people. None of them are “put on spurs” (though I have to question any trainer that doesn’t have someone going in the ring to jump without both spurs and a crop–I don’t remember the last time I’ve shown over fences without both of those, it’s as much a part of show attire as gloves and a helmet).
Get a vet out to evaluate the horse that knows something about lameness. Even horse vets will admit that this is not all of their strong suits. There are vets who concentrate on repro, who are good at fixing wounds, and who are freaky good at pinpointing lameness. Find one of the latter; most good vets know what their strong point is and will happily recommend someone else to you who they know is good at the problem you’re having if it’s not their thing.
Get weight off the horse. Not by riding it every day, which is only going to exacerbate any pain issues it might be having. Drop down to 4-5 days a week, and only jump one of them. And certainly don’t do two jump schools in one day!! If you’re also competing at dressage, really focus on the flatwork, it will only help the jumping anyway. Especially work on getting him off the forehand. Put a muzzle on the horse for turnout, and get it a small-hole haynet for when it’s in the barn.
Get 4 shoes on, with bell boots up front if he pulls shoes. That’ll help fix the underrun heels you say he has up front, and provide more support up front and behind. My horse generally gets hind shoes pulled in the winter, and is noticeably happier in the spring when they go back on, to the point that I think this was the last winter they get pulled. I want the horse to be comfortable and happy to work, not worried about guarding a joint or foot.
Get a loading dose of your choice of Adequan/Legend/Pentosan, and put him on a real joint care regiment. If this horse was started as a reiner, he’s been working those joints hard for probably 10 years. They need some help. See what that does for him, and you may be able to put off injecting the joint for a few more years.
Then evaluate your riding. Everyone rides differently in the show ring than they do schooling at home. Get someone to video, sit down and objectively evaluate yourself a few days later, after the emotions have faded. See if you can pinpoint changes between how you’re riding at home versus in the show ring. Make sure you’re RIDING in the show ring and not just being a passenger, because you’re worried about it looking “pretty.”