Hi, Welcome to JustAnswer. I am a licensed veterinarian and I'm here to help you. I'm sorry to hear that Lloyd isn't feeling well. Yes, this could be a cold! For this you can gently clean off her nose and her eye with a warm moist towel 2-3 times daily so that she can breathe better. Also, it is a good sign that she is still eating. If her appetite drops off, then warming up her food to bring out its fragrance sometimes help. . .if they can smell the food better, they are more likely to eat.
Since colds are usually a virus, add 250 to 500mg of lysine to her food daily may help. Lysine is an over the counter product that is available at pet stores, or on your vet's shelves.
Often, however, these viral colds will open the cat up to a secondary bacterial infection. In this case, Lloyd would need an antibiotic. If her symptoms continue for a few more days, or she grows worse, then I'd have her vet check her out and probably start an antibiotic. Also, since only one eye is involved this may indicate that she has a URI caused by a chlamydial infection. . .a bacterium. . .that would be best treated with an oral antibiotic and an eye ointment.
Hope this is helpful. Please continue our chat if you have any further questions or comments!