No, salt baths will not do it; you will need medication to treat anchor worm. And it should be done quickly, as these nasty creatures burrow deep into your axie's muscles, organs etc. The deeper they get, the more damage is done when they are removed. Some people try gently pulling them out, but this is not recommended, as it can cause a lot of bleeding (and infection), you may not get the whole worm out, and it involves handling your axolotl in ways only an expert should really attempt. You definitely should go to a vet for this one. And as Hayley says, fridging is not indicated.
Also, as an earlier post noted, you will need to sterilise everything in your tank. Which of course means re-cycling your tank, preferably without the axies in it (it will need a source of ammonia though), as they will have suffered enough stress from the anchor worms and would probably be better off in tubs of cool, dechlorinated water with 100% daily water changes while recovering. (By the way, is your small tank cycled? It doesn't sound like it would be, and you don't want to put anything from the infected tank into the new one, so if you do transfer them into that tank, you'll have to do major daily water changes and monitor ammonia, nitrites and nitrates carefully.)
And yes, these anchor worms would definitely have come from the unquarantined feeder fish. Always quarantine anything (plants, fish) for at least a month before adding it to your axie tank.