Unfortunately, it sounds like botulism or lead poisoning. Either way, the swan will not be able to hold its head up because of involvement of the neck muscles and central nervous system. If the swan can walk, then it may be lead poisoning, if it is unable to walk, it is botulism.

Hopefully, we are wrong on all accounts, but if either is the case, the bird will eventually die, especially without treatment. Usually death is from drowning, not being able to lift the neck out of the water or paralysis of the central nervous system which will eventually affect breathing and swallowing. The Regal Swan