The Snake is dead, so obviously he/she did not get the advice he/she needed. Respiratory infections are the cause of most snake deaths in captivity. I did not hear one person suggest raising the temperature or giving antibiotics. I read through this entire thread and I don’t know anything about the husbandry condition the snake was in. This would be the first thing that I would want to know before suggesting anything. The snake was eating at one point, so a medical cause seems to be the most likely cause of her symptoms and eventual death. I have never heard this clicking noise, but any sounds while breathing are suspect of a respiratory problem. If the nostrils get clogged, which causes noise, it is usually due to discharge and foreign material clogging things up.
A huge clue was the obvious medical problems a sibling had at the Pet Shop. Corn Snakes have to be kept is some pretty bad conditions to get respiratory infections or sores. It definitely sounds like somewhere in the chain of possession of this snake, there are some problems.
I have been to wholesalers places of business and have sold lots of snake to them. Some are good and some are extremely bad. Mixing a bunch of animals together in a very confined place from multiple sources is certainly not the best of situations and can very easily spread disease around. There are some very bad #$%& out there that is not treatable and can wipe out entire colonies.
Pet Shops can be good and bad, the same way that wholesalers can be. There are 1000’s of breeders of Corn Snakes on this forum. It seems like a good idea to me to remove as many people in the chain of possession, and possible exposures to other reptiles that may be carrying a disease, and buy direct. Pet Stores can do the same thing.
I have lost many snakes over the years for a variety of different reasons. I know that I could have saved some of them, if I would have not waited it out. Some snake just want to die for some reason as was stated above. I lose a lot of my hatchlings from starvation. Perhaps it is natural selection in captivity. Raising the temperature 5 degrees or more increases the snake metabolism a lot and will help the snakes own immune system fight the problem. This is always the first thing that I do. Snakes generally recover very fast, if the treatment is appropriate. If there is no change in the condition very soon , another approach should be taken. Antibiotics can work wonders on many problems, especially respiratory illness. Raising the temperature and administering antibiotics is a very good first step to take in most situations. Sometimes it is just too late and nothing will help.