Hey there Burnie9, it's as Ivaristal said. The sickness message can stay for a little bit when you freeze the hatchling but it can't die, since they are treated like adult dragons.
From the FAQ on the forums:
Q: My frozen hatchling is sick, will it die? A:No, frozen hatchilngs are treated like adults in that they cannot die unless you hit the "kill" button. Your hatchling will most likely get better eventually, but it is no big deal if it doesn't.