How do I keep the fruit on the tree from having worms?
I have a pair of abundantly healthy 4 year old peach trees that yield about 20 pounds of fruit each and I too had that problem the first year. I found a professional Fruit Tree Spray Concentrate by Bonide. Granted it is not an organic solution, but it is effective for sure. Just use extreme caution; DO NOT spray any of the fruit until ALL of the flowers are gone and the fruit has started to develop. This product will kill honeybees if you apply it while they are trying to pollinate the tree for you. also liberally spray the branches and the trunk of the tree to help eliminate the travel path for those pests, and keep reapplying every 2 weeks as directed on the bottle. Additionally you should cut back any other tree or plant limbs that are touching it. here is a link to the product that I use. It should be available at your local hardware store.
Hope this helps.
A regular spraying schedule is important to prevent pest and disease.
Here is a link with more information.