While waiting for the answers to my questions above I figured I would post this to help in the meantime.
If she is showing any symptoms described in this question, then she is indeed choking. It sounds to me like this isn't the case.
If not, and taking into account her age, she's probably experiencing mild respiratory distress. All rats have a certain degree of mycoplasma, which causes something akin to chest infections in humans. It can happen throughout their lives, or it can happen only as they get older. She will need a vet to assess her further and listen to her lungs to determine whether it is 1) a treatable infection, or 2) sadly a result of very old age. The vet will likely prescribe antibiotics for the former, but there is little to be done for the latter beyond making her comfortable.
To alleviate the symptoms in the meantime you can: make sure she is in a well ventilated room, keep her warm, and feed her dark chocolate (mine are partial to Bournville, though you may want something closer to 70% cocoa) which will help open up her bronchioles. Methods detailed here may also help her out, though these are typically for more severe respiratory distress, but always worth a try.
I hope she improves!