Hi, I am not an expert but do have a horse with challenging feet.
My horse is a senior and had many years of bad hoof care so she will be in glue on shoes forever. But your horse is young. I would think that you could use them transitionally till the hoof improves. If needed. If they didn't stay on they probably were not applied with the right amount of preparation done to the feet. You need a hoof person that does several glue on shoe horses a week, not rarely. You also have to make sure that the feet are being trimmed properly before the application.
If that horse were mine, I would first try getting a good barefoot trim and then ordering a pair of pasture boots like the easycare clouds and then also getting a pair of riding hoof boots such as the gloves and have your farrier heat fit them to your horse.
I would make sure your horse isn't stalled and has room to constantly roam a bit. I would avoid grass pasture and stick with grass hay and supplement accordingly. You can use hoof supplement such as biotin but results won't be seen for around 9 months till the new hoof has grown out a bit.
There are hoof people on here that can advise you better on diet and hoof care.
If it was me, I would have a vet out to examine for the lameness.