Hi, have you been able to contact your diabetes nurse/team?
Some thoughts (given I'm not a doctor!). How would you describe how much carbohydrate you've eaten over the past few days/week/weeks? Very low carb? Have you been exercising lots/ill and eaten low carb? It is possible to have ketones with normal/low blood glucose values. They're produced as a byproduct of the breakdown of fat to release energy, so if your carb intake has been low it could explain what some call 'starvation' or 'nutritional' ketones (also seen if people follow 'extreme' diets). This is often the case if people are ill and lose appetite so don't have as much insulin.
Other thoughts: have you tried different ketone or glucose strips/different batch or tube? Do you have any back up meters to verify either results for glucose or ketones? Is the ketone test via blood or another way?
I hope you've managed to get in touch with your diabetes team, and are remembering to drink plenty of water to try and flush the ketones out. I also hope you obviously steel better soon!!