I think my cat has a respiritory infection. How can I help her at home?

I would call the vet and tell them what you've just told us here. A cat cold is very serious and she needs antibiotics. I don't know of any home remedies for cat colds and human meds are usually poisonous for cats. The watered down chicken broth is a good idea, and you could take her into the bathroom and run a hot shower for the steam, maybe that would help her breathing. Other than that, she needs the vet (getting the antibiotics is more important than the chances of her picking up an infection). I'm so sorry your kitty is sick, and I wish you all the best.