Hello and thanks for trusting me to help you and Nayla today. I am a veterinarian with over 25 years experience and would be happy work with you.
If she was just laying in the chair right before this happened and was fine before that, the odds are it is not a traumatic injury of any sort unless she perhaps injured it or somehow twisted it before and it started to hurt later, but that would be odd.
It is possible she has something lodged in between the toes or the footpads or that she has torn one of her nails, but if she won't let you look, it may be difficult to evaluate that. Try to monitor if she is licking at any particular area of the foot. Maybe she will let you soak it in some warm water? Could she have perhaps stepped on something hot earlier and burned it? If she won't let you soak it, maybe she will allow you to apply a cold compress.
At this age, I guess it is possible that she could have some sort of congenital abnormality affecting either her knees or hips and something may have slipped out of joint. Again, that would be kind of odd.
Unfortunately, there is not much more that you can do for her at home. If she will let you get a glimpse of it, I would look for any signs of redness or scaling of the pads. I would not advise that you offer any sort of over the counter meds for pain that you may have access to as most are not safe for use in cats.
I hope this is helpful. My goal is to provide you with excellent service – if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate me when you are done. Thank you for allowing me to assist you.