Yes, your kitten has caught cold for sure. It is caused by a virus that s Feline Herpes Virus. Isolate your kitten and avoid contact of other pets with it. Humans don't catch this disease from cats so no need to worry about you. As a home remedy you should provide its heat through pet-friendly Eucalyptus Oil burning in its room. Take extra care of your kitten as this cold can be turned in to high fever, which is then difficult to handle, though not impossible. If your kitten recovers, after making these measures, in a day then it's fine. Otherwise, take it to a vet who will suggest antibiotics and your kitten will be fine soon.
