Start him on Adequan or Ledgend injections and KEEP him on them. Adequan is IM. Ledgend is IV. Both are prescription drugs but are very effective. These ARE NOT joint injections.
Once you start a horse on them, you should keep them on them. Both help the horse keep good lubrication within the joints and can delay major arthritic changes for several years in some horses.
You can also use a joint supplement like Cosequin or Fortaflex. A lot of people swear by them. Personally I would use the injections first and would do both or either before I went to Cortisone and/or Halyuronic Acid joint injections.
Get this horse over hurting now. The longer you run him with pain issues, the more prone he is to getting arena sour or will start blowing barrels. Bute is a poor substitute to actually treating joints and actually speeds up drying out joints which in turn speeds up arthritic changes.
I would use a good lameness Vet that specializes in barrel horses, reiners or cutting horses. THEY are the hock and stifle joint experts.