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Your vet should have known. I'm not an expert, but what you medicate with may be unique to the type of worm. However, the worms I have dealt with are common and known as "Gapeworms". Here's a link to help you identify if it is Gape...http://en.wikipedia.org/wiki/Gapeworm

Gape is easily seen though. Birds will constantly breathe heavier. The biggest thing to look for is birds that appear to be gasping for air. They may also seem lazy, and you may even be able to walk right up to them and pick them up. To fully diagnose Gape, take a bird that appears sick and cut the windpipe open so it looks like a hot dog bun. If you see worms (red in color), you know they are the problem; blocking the airway and basically stressing the birds to death.

I treat this by having my vet prescribe me Panacur. Panacur is a de-wormer that can be bought in both liquid and powder form. See directions for administering it. I simply mix the correct amount into 5 gallon buckets of water and pour into calf buckets. Don't forget to cut off any other source of water to make sure they drink medicine.

Preventing worms in general can be a tough thing. Moisture is a key for worms to get into your birds. Drain out or cover puddles with straw to keep birds drinking good water without worms. Other small birds can die inside your pen and bring it in. Canibalism doesn't help. Botchalism (probably spelled wrong) is also bad. You can lay straw around feeders/water to cover up the bacteria where they are eating/drinking. Giving birds space helps with everything.

what are the advantages/disadvantages on raising on wire vs on the ground?