Could be many things, of course, as others have mentioned, but I'm wondering too if the problem could be in his neck/spine since that's where you noticed a slight pain reaction. I had a similar problem with one of mine who as it happens was also 3 at the time. He would limp intermittently on a front leg after hard running or heavy playing. After a period of rest, lead-walking, painkillers, muscle-relaxants etc he would appear to be better, but the problem would again recur after running or heavy playing.
Our regular vet had no idea what the problem was so we took Sunny to see a very experienced greyhound vet, who found that the problem was a slighly misaligned vertebra at the base of his neck, just about where the shoulder blades meet. Apparently the misaligned vertebra causes pressure on the ulna nerve and thus causes pain and lameness in a front leg. This vet has a lot of experience with racing greyhounds and told me that it's a fairly common injury but often overlooked by regular vets.
We treated Sunny with chiropractic and it took a few sessions but he gradually recovered and now generally only needs a couple of sessions a year just to check him over.
If the problem keeps recurring despite rest and anti-inflammatories, and your vet can't find the problem, I'd consider getting an opinion from a vet experienced in treating greyhounds if you can.