You should probably consult with the vet that did the injections. Response to injections, or lack of, is an important factor in determining what the problem is. I'd give the vet a call, at least, and they can weigh in on whether to give bute and how much. If the horse is more sore than before (not sure from your post), all the more important to involve the vet.
I'm thinking 2 grams 2x day for a week, then 1 gram 2x day for another week.
Is this too much? Not enough?
Your vet should be the one to answer this question, not people on a BB (although many here are very experienced) - no one here has SEEN your horse. What is a "very sore horse" to one person might be "he's not too bad" to another.