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Chihuahuas are a difficult breed with their eating. You do need to make sure the dog's blood sugar remains normal. I recommend a vitamin paste that you can get from your vet called NUTRICAL and should be given daily. You may try warmed baby food (meat) and see if the pup will take it...it is bland and shouldn't cause tummy problems.
Well, the puppy can have a virus like corona or parvo. Parvo is an aggressive and potentially fatal gi virus. It doesn't sound like your puppy is that sick.
The nose is not a good indicator of health, but if the puppy is not getting enough fluids for what the puppy is losing in the diarrhea, dehydration maybe a big factor.
You can try pedialyte...but I really think you should get the puppy into a vet soon. These little guys are so sensitive and can only handle so much in dehydration. The vet will run a fecal to make sure this is not from a protozoan (not treated with the dewormer you gave).