What you are describing may be "keto breath". Low carbohydrate diets (including fasting) can switch your metabolism from one that digests sugars to one that digests fats. (That is a vastly oversimplified explanation but there is a vast amount now written about "ketosis" and "ketogenic diets" that you can read for more details.)
First, to determine whether that is what is happening, you should get a test. You can do a somewhat accurate test at home with strips that test your urine. There are numerous brands available through online retailers. You should only purchase the amount that you think you'll need in the short term because the strips degrade on exposure to air. For a more accurate test, you can get a blood test or a breath test from a medical professional.
Second, if the issue is ketosis and keto breath, there is little you can do about it. You should try increasing your intake of water, which may help to divert the ketones in your bloodstream to your urine instead of your breath, and may also help to keep your mouth hydrated which will reduce the activity of bacteria that may compound the problem. You could increase the amount of carbohydrates in your diet, but that is probably not the solution you are looking for (unless there is a medical issue that precludes fasting, which is maybe something you should discuss with a medical professional). You can try to mask the odour with low carbohydrate candies, chewing gum, and mouthwash.
If you look up "keto breath" online you may find other advice, but I haven't found much other than the above, and "wait for it to reduce on its own".