Why would you be reluctant to get a vet out? If your horse is suddenly unsound when he was sound you absolutely should get a vet out
I usually wouldn't be to quick to judge but I honestly would get him checked out. My horse was fine straight to the left but to the right she was completely off. It started getting worse as times went on and we got her checked, despite others telling me she was fine, and she turned out to have an injury that now has stopped her from continuing jumping(although this is very unlikely injury and we were just unlucky that it was this bad) If you personally feel like your horse is not acting right, then follow your gut because better safe then sorry. Good luck and I'm wishing all the best for your horse! :)
He could just need more work on that lead. And it could be his balance like Sharon said. Maybe lunge him going to the left. Wish u luck and hope it doesn't get worse!
It just might be his balance. I don't only ride one horse all the time so I notice that the horse might be a little off balance it the trot or canter on the right circle or left. If it gets worse than you should see a vet. It could be serious. (what I said probably doesn't make sense but I hope this helped anyway)