How old is your kitten? The younger the kitten the more fragile. And I have no experience with kittens younger than 3 months of age.
In kittens several months old, and adult cats, a URI is often not very serious- and it is extremely common for shelter cats to have them. They are often caused by viruses, in which case the antibiotic won’t help; although coughing up thick gunk sounds to me as though it could well be bacterial. How many days are you to give her oral antibiotics? And are you successful in getting her to take them? Is she still coughing? If she is no longer coughing, I would think that that is a good sign- the infection is moving out of her lower respiratory system.
Meanwhile, while the antibiotics are working she needs supportive care. Closing her in the bathroom while you run a nice steamy shower may help decongest her. She is probably not eating much because she can’t smell her food while congested, and so it doesn’t taste good. I would try giving her moist food, and warming it gently in the microwave beforehand. (Before you give it to her, mix up the food thoroughly and test the temperature on the inside of your wrist- it has to be just warm, no hot spots that will burn her mouth!!!) You can also try giving her some tuna juice as it is nice and smelly.
If cats don’t eat for 2-3 days, they can develop fatty liver disease, which can be fatal. So make sure that she is eating something. Also, dehydration can be a problem; check this thread for the ‘tent test’ http://www.dailykitten.com/chat/topic/31106
You can always call the vet, explain that you are a first-time kitten mommy and ask them what they think- is this normal progression or worsening.