There could be several reasons.
First, many cats do not like being picked up. So the question is, is this new behavior for her, or has she just recently started objecting to being picked up?
Could she be in pain? If you gently touch or move different parts of her, well you’re not picking her up, does she suddenly react? If it seems like she’s in pain, or you’re not sure, that would beworth a trip to the vet.
How did she act when you pet her? How is her walking? Is she eating normally? How about her bathroom habits? Is there anything else about her behavior that has changed? These are all things that the vet will want to know.
A 14-year-old cat is getting up there in years. It would not be surprising if she was developing some kind of problem. I really think you should take her to the vet.