His foot is less red, less swollen, and he can now limp on it. That's improvement. It is getting better... maybe not overnight... but it is. You're right that the infection needs more time to completely go away.
He should be religious about taking that antibiotic exactly as directed. He should not miss any doses and should take them on a regular schedule. Even if the pain is barely there two days from now, he still needs to continue taking the antibiotic until it's all used up - or else the infection will return, and it probably will be even worse then.
If the infection, with its redness and pain, isn't mostly gone in the next 2-3 days, he must return to the ER for stronger medicine. I don't want to scare either of you, but he could lose his foot - or even his life - if this infection isn't completely eliminated soon. It's clearly nothing to dilly-dally around with.
I hope he feels better ASAP!