yes. you have 15 amp 14/2 with no ground. you should have a grounded
outlet for your washer.
appliances like this are designated to be connected to a separate
grounded circuit. white is supposed to be the ac common, and black the
hot. by changing to a 15 amp gfi you will overcome the shock hazard
from the ungrounded washer and keep the cat safe. if it pops when you
plug the wahser into it your washer had an undiscovered shock hazard.
an ac radio will help you find an unmarked breaker.