You should ensure your kitten gets plenty of rest in a warm, comfy environment. Also, she needs to drink a lot of water to compensate for the lost fluids. You can try using a humidifier to help your cat breathe easier, and to encourage her to eat.
If you suspect that there's a foreign body in your cat's trachea, you need to take her to the vet immediately. The veterinarian will probably recommend to hospitalize your cat, to be able to closely observe the process of the foreign object in her trachea.
There’s also a chance that a cat that sounds congested and shows no discharge will have a heart disease. A cat suffering from a heart condition will have trouble breathing, since the fluid will be accumulated in her chest cavity.
Proper treatment in the early stage of the heart disease will decrease the chance of further damage to a cat’s heart. The vet will undertake chest x-rays and a heart ultrasound to determine the exact state of heart disease in your cat.