Fruit Sugars

My sugar limit in my calorie plan is 33 grams. I typically eat at least two servings of fruits day, if I am unable to do more. When I buy apples, for example, the facts say that the apple has well over 25+ grams of sugar. I noticed when I added a cup of grapes to my diary today, pretty much every listing in the database shows a cup of grapes containing 30 grams of sugar.

If I didn't eat fruit, I would be under my limit, since I average only about 5 grams of sugar per meal. But just by lunch time, my sugar intake would be already over my limit if I included fruit in my meal. I know fruit sugar is better than processed sugar, but what should I do about this?

I like fruit more than vegetables. I've tried to eat more veggies, but they make me sick. I can only do lettuce on my sandwiches, or a basic small salad with not a lot of toppings. I don't have the stomach for a lot of veggies. I can tolerate corn, peas, green beans, but not a lot of other ones.

How can I help my sugar intake, without eliminating fruits all together? Pretty much one apple sends me over my limit.