Is the swan shaking its head after it has been in the water or this consistent behavior? If this is consistent behavior, regardless of swimming or getting wet, the swan may have an ear infection or ear mites.

We think that you are located in England. If so, please contact the RSPCA or Wendy Hermon at Swan Support (Datchet, UK) to see if they can come out and assess the swan. If you are located in another area, then you might contact a local wildlife/waterfowl rescue/rehabber to see if they can get out to check on the swan. If the swan can escape by flying or the area is inaccessible to rescuers, then there is not a whole lot that can be done. The above contacts should still be made to see if something can be done. The Regal Swan