I have never noticed a difference until about the two week mark and with some injections it has gotten worse before it's gotten better. I find usually it's when I think it hasn't worked that it starts working. All this will depends on what you're putting in and where but I would wait at least two weeks before you start worrying that it's not working.
Always been immediate for me (after 4 days off plus equiox/previcox). Then continued improvement until 2'weeks then some go down hill pretty soon (usually when hocks are a secondary issue) or they stabilize for several weeks or months.
I think 2-4 weeks is usually how long you should allow before making any judgements about how well the injections have worked. I just had my older horse's done, and he got 2 days off, 2 days of light work (vet said "light hacking") and then back to full work on day 5.