I have dealt with naval / joint ill many times.
Has the antibiotic been injected directly into the joint(s) affected? They must be treated directly into the joint.
The usual method (and the way our Vet has successfully treated it) is to do 2 or 3 joint lavage treatments using saline mixed with the appropriate antibiotic. One large needle is put in one side of the joint (the side facing down as the foal lays there and an IV bottle with the antibiotic / saline mix is run in another smaller needle on the opposite side of the joint. When clear saline mix is coming out of the big needle for a good while, it is pulled out and one person keeps pressure on it to prevent leaking. A pure antibiotic is then injected into the joint through the smaller needle and the joint is wrapped. If you are treating a knee, the leg should be wrapped from the hoof to above the knee and the top of the wrap should be held in place with duct tape or Elastikon.
We have had the best response when our Vet used Crystalin Chloramphenicol It mixes readily with warm saline if you know how to do it. [It 'glumps' if you don't do it right.] A compounding Pharmacist can make a Chloramphenicol paste to give orally (we used 1 gram 2 x a day). When the joint stops building fluid and the temperature comes down in the foal and the last lavage was clear from the start of it, the foal is ready to go on 10 more days of oral Chaloramphenicol.
Our Vet highly recommended injecting the joints of the foals treated after they got all better. He used Hyaluronic Acid because he said if you did not, they seldom held up to training. Some of them don't anyway -- even if all fever, high white counts and swellings completely disappear. After a joint infection, the joint fluid has a lighter viscosity and that should be addressed with HA injections.
If this foal has gone more than 1 or 2 days without very powerful antibiotics injected directly into its joint, it may not ever be sound or get much better. These things really need to be treated very aggressively and very early.
I probably do not have to tell you that this is a very grave condition with a 'guarded' to poor prognosis -- especially if it was not treated very early and very aggressively.