I'd definitely bring him to see the PD or a GP just to be sure there's no fracture, since he's still limping quite a bit and the swelling is pretty significant. Once you've ruled that out, most ankle sprains do settle with rest, ice and elevation, though some parents I know have found physio helpful if the limp doesn't improve after a week or two. Recovery usually takes anything from a couple of weeks to a month depending on how bad the sprain is, so it's worth getting it checked early so you know what you're dealing with and can plan his activities accordingly.