Did a vet actually prescribe these antibiotics for the boarding place? How long has she already been on them? I find this situation a bit concerning. Here's why:
Lethargy and loss of appetite are very common with a bad case of kennel cough in dogs with compromised immune systems I see from the shelter. However, those symptoms are less common in a healthy pet dog though (a healthy pet dog usually fights off KC much better than this).
In very sick shelter dogs, I see the loss of appetite and lethargy routinely set in with GSDs within a couple of days of onset of the first symptoms--it hits hard and fast in the shelter. When did her symptoms set in during boarding?
My worry with KC with a very sick dog is always that it has the potential to turn into pneumonia, which can require intensive care (round the clock) to come back from, as it's life threatening. My inclination would be to take her to the vet tomorrow AM to be sure this hasn't turned into pneumonia (warn them you are bringing an infectious dog, though, as they may have you come in through a side entrance to avoid spreading the KC in the lobby).
My experience working with kennel cough in shelter GSDs is that they don't bounce back without antibiotics once they get lethargic and anorexic -- but they bounce nicely in 3-5 days with the right antibiotic (Doxycycline is what I'm always told is the drug of choice for an upper respiratory infection here). I'm glad you've already got antibiotics on hand for your girl.
Lots of things to think about here:
1. Keep her warm, in the house (not outside or in a garage). If you have an essential oil diffuser, put eucalyptus in it. If not, use a vaporizor and put it in well (or use Vicks inhalant in the vaporizor well, just like with a sick child).
2. Is she drinking water? That worries me way more than loss of appetite. If she's not drinking, she may need to be given fluids (again, vet trip -- no later than tomorrow AM). The dogs often feel a lot better after a liter of fluids, and then the appetite comes back a little.
3. If she's lethargic and not eating, you've still got to get the antibiotics down her. However, Doxy on an empty stomach seems to make them feel yucky.
Food already isn't interesting due to the mucous, so you will need some super-high-value yummies to tempt her to eat -- cooked chicken liver, Natural Balance log, canned food, whatever her favorites are that will tempt her to get a little food in her tummy will help.
I've sat in a shelter with a tray of "Cesar" brand food for tiny dogs (junky but appealing), spoon-feeding a sick GSD who was like this because it was the only thing that dog was interested in eating. I don't stand on principle with a dog like this-- I need to find something to put in their tummy so the Doxy isn't on an empty stomach.
Also, worst case scenario, there's a technique we've used with a few fosters of gently placing it in the very back of the mouth and holding the mouth shut for a second or two (the dog almost always swallows right away), but have someone who knows how to do it (vet tech, for example) show you how to do it so you aren't struggling with your dog, and you have to really trust the dog. I really don't like doing this though because of the way the antibiotic hits the empty stomach.