Yes, there is definitely an injury to the bill, not sure without examination if the bill will heal or if the injury will impede feeding. As long as the cygnet can open and close its bill to feed, this should not be a problem. Also, just as in any young, certain tissue is not fully developed into its eventual adult thickness or stiffness. An example would be the bone structure in the young of humans that it is very soft around the fontanel area of the skull that eventually ossifies into bone.

Even though the bill is somewhat soft in adults, it is not as soft as in the young. Eventually, the bill will somewhat harden as the cygnet grows. Hopefully, this injury was in such a location that it will harden as normal and not affect the opening and closing of the bill.

As far as peeping, this sound alerts the parents to the location of the cygnets as well as a form of communication which may also signal stress or feeling of fright in the young. So, during or prior to a fight or intrusion by a predator or other species in the cygnet's territory, the peeping could certainly increase. The Regal Swan