My cat is vomiting, has soft stool, and is quiet. Should I worry?

I'm sorry Minx isn't doing well! I would not be concerned about her nose being warm and dry. The temperature and moisture of the nose is not used as a sign of illness in cats. That's because it can go from cold and wet to warm and dry just by lying near a heat source or in the sun. It is concerning that she has vomiting, had soft stool, and is now quiet. She could have a GI illness, may have eaten something rotten, could have a foreign body, or could have pancreatitis. I can give you a home remedy to try to see if that helps. I recommend withholding food for 12-24 hours, then feeding a bland diet of boiled white meat chicken (no bones) in small amounts several times a day for a couple of days. Then slowly add back in her normal diet. If the vomiting continues in the absence of food, she vomits the bland diet, develops diarrhea, stops drinking water, starts vomiting water, or becomes very lethargic, she will need to see a vet right away. Good luck, I hope this helps!