I'm so sorry Libby has all these symptoms. They can all indicate different conditions or all be related to the same problem.
Due to her senior age, her lack of appetite, weight loss and lethargy can be signs of untreated diabetes, a thyroid problem, liver or kidney issues. Older cats are more prone to develop these diseases.
Her sneezing and coughing may indicate the beginning of an upper respiratory infection (kitty cold) or it can be a symptom of feline herpes virus (different from human herpes). For the moment, you can run a humidifier in the room she spends the most time in and start giving her herpes medication made for cats, like Viralys. Here is more information:
If she's licking herself excessively, causing hair loss, she may have a condition called feline psychogenic alopecia. This can have many causes, one being stress. To reduce stress get a Feliway plug in, which emits calming pheromones. Here is more information:
If her stools are loose and sometimes contain blood, this is a serious symptom, indicating there is a problem in her intestinal system or she may have allergies to some of her foods.
There are so many symptoms, that Libby definitely needs to be seen by her vet or any vet in person, as soon as possible, to be evaluated, diagnosed and treated. Blood work, urinalysis and a fecal analysis will be done to provide more diagnostic tools for the vet.
I hope all will be well with Libby! Please let me know how she's doing and what the vet's findings are. Thanks!
Please be so kind as to rate my answer with positive feedback from the ratings box at the top of your page; that is the only way I receive recognition from the website for my effort and assistance. Thank you very much!
Providing a positive rating will not end our conversation, should you need me for any follow-up. Simply click 'Reply to Expert' for clarification and/or additional information, if needed, at no additional cost.
Please don't hesitate to request me by name, for any future questions; just type: "For Cher Only" to begin your post.
Bonuses, although never expected, are always welcomed.