This sounds a LOT like my guy, including the being referred to as “cold backed.” The girthy part could be a sign of ulcers or other tummy issues. This will also cause anxiety and what other horse people around you to call “bad training” and tell you to go back to basics. If you KNOW in your heart your horse’s basics don’t have any holes, and he was fine before but seems to have suddenly “forgot” his basics, I would look into tummy issues.
My horse was toted as “hard to handle” and having “bad manners” or my favorite was some people called him “high strung.” There is a youtube video that can show you some of the pressure points that can signal ulcers. I did this and my horse went nuts. I called the vet and he was treated for ulcers. Then he switch to SmartGut, and then SmartGut Ultra when it came out. For 2 years my horse is nice, normal and CALM. I also pair it up with SmartCalm because ulcer treatments can lead to magnesium deficiency. This causes all sorts of behavior issues too…google “magnesium deficiency in horses” and you’ll see what I mean.
With both the SmartGut Ultra and the Smart Calm, my horse is AMAZING. We are also at a new barn where he is handled by young 4H’rs all the time and is a favorite. When I told my current barn manager what his reputation at his old barn was, she couldn’t believe anyone would think that of my horse.