What really matters is your blood sugar. If you have normalized your blood sugar then there is no problem eating. Your body will just dump the ketones and you will be fine. But if your blood sugar is 400 mg/dl and you have ketones, you should not be really eating, particularly not carbs. You just won't be able to properly bolus and eating will likely raise your blood sugar further increasing your risk of DKA. Does that make sense?
Ketones occur when we burn fat. Being sick, it is not uncommon to stop eating and you will burn fat, thus you generate ketones. While you won't usually generate high levels of urine ketones when sick (you might), you may well see marked levels of blood ketones. Did you measure blood or urine ketones?