Bless you for taking such great care of Nala even though she has seemed ungrateful.
You are doing the exact right thing. It is more stressful for her to be outside sick than to be confined in your garage with you and a cat she trusts.
Anytime a cat stops eating she is either sick or in pain.There are many things that can affect 13 year old kitty that lives outside.
You can try a few things to calm her down and perhaps get her into a carrier to be seen.
Get a jar of turkey baby food with no onion or garlic. Or a can of little friskies turkey and giblets pate food. Turkey contains l-triptophan and is sleep inducing.
Add one quarter of a 4 mg chlortrimeton to a tablespoon of food It is a teeny pill sold OTC near benedryl. She will not detect it in her food but it will make her sleepy.
Put more food all the way in the back of the carrier. Totally ignore her. Make believe she is not even there. When she goes into eat calmly close the door. Then just take her to the vet. Keep the carrier covered in the car to keep her calm. Please let me know how things go. Reply here or if you prefer we can speak on the phone.
Please be so kind as to rate my answer with positive feedback, as that is the only way I receive recognition from the site for my assistance. Thank you!
Providing a positive rating will not end our conversation, should you need me for any follow-up. Simply click 'Reply' for clarification or additional information, if needed and I will always be here for you and your kitty.