Welcome to the Forum!
You can have fruits, but make sure of what you choose. Different types of apples, for instance, have different carb values. Some are very high, in grams of carbs, while others are some what lower. In short, choose your fruits well, I try to stay away from bananas, as they are very bad for me. Your Mileage May Vary (YMMV).
Have you considered celery as a snack and maybe kick it up a notch with some peanut butter or low cal cream cheese. Or you could try, in moderation, dry roasted almonds at 5.5g carbs per ounce.