No fish cannot live inside a whale.
if a fish gets swallowed by a whale the fish my live for maybe one day at the most before it dies because it has no air to breathe or oxygen from water.
The fish would also be digested by the whales digestive acids inside it's stomach so eventually it would die even if the fish were able to breathe.
The digestive acid would kill the fish either way.
Whales have 4 stomach chambers that are full of digestive enzymes so the fish would not be able to survive.
Even if a human got swallowed by a whale the human would eventually die as well because there would be no fresh air for the human to breathe in.
Also the human would have no food and the digestive enzymes would digest and break the humans body down for food.
The same with the fish it would be digested.