Aloha! You're speaking to Dr. Michael Salkin
Vocalizing when lifted is one of the signs of back pain in small dogs - in particular, the pain associated with degenerative disk disease (a "slipped disk"). Shaking, trembling, reluctance to jump up or down or navigating steps, a change in posture - a "hunch" in the back and/or holding the neck rigid and head low - and a normally social dog becoming aloof or, conversely, a normally aloof dog becoming "clingy" are supportive signs of a disk.
Her vet can careful palpate (feel) your Chihuahua's spine for areas of hyperpathia suggestive of a disk and, if present, initiate therapy with a nonsteroidal antiinflammatory drug such as carprofen or meloxicam, a skeletal muscle
relaxant such as diazepam or methocarbamol, and a narcotic analgesic such as tramadol. X-rays may be recommended but many of us will rely on the findings of our physical exam and treat presumptively.
Until she can be attended to, it's best to restrict exercise and discourage jumping. If she became paretic (weak) or a limb became paralyzed, she should be seen by a vet at your earliest convenience. I don't believe that her behavior
is related to her diet. Please respond with further questions or concerns if you wish.