If he’s eating fine that is a good sign. No need to starve him.
Signs of internal injury will vary depending on what is actually injured. You will need to monitor/observe your fish. Any internal organs could potentially be at risk after such ordeal. Swim bladders, kidneys, stomach, or even head and spine. Some general signs to watch for will be bruising, swelling, unusual behavior, dulled appearance, labored swimming/ breathing, un responsive behavior.
If your fish is currently not showing any negative signs besides the split tail fin, you likely won't have to deal with other problems. Sometimes it just helps to be mindful of the potential injuries that can occur to prevent it from happening again.