I am pretty sure a 3 month old wouldn't be mating and that's what usually causes a prolapse but if you can catch and post a pic it would help alot . Maybe just something he/sh ate it shouldn't have and is having trouble coming out?
That is his penis so you have a boy, they may not let you pick them up but you need to with this one, if it gets infected you could lose him. He must be old enough to mate and has over done it. He needs to be wash real good and then slathered with something lik Prep H or Manuka Honey and try to push the prolapse back inside and he also needs to be kept away from the ducks for at least 1 month to give this time to heal, if there is already infection then he'll need to be seen by a vet and most likely have the dead cut off and be treated with antibiotics. But first catch him and see what it looks like up close. A drakes penis is cork screw shaped can't miss what it is. Hopefully you'll be able to treat him with out anything else needing to be done but time is very crucial right now if you hope to help him.
Sorry such a bad pic but my ducks won't let me pick them up.
