Apple's and peaches are the two hardest crops for us to grow.
What we are seeing is one of many soft rots the fruit are susceptible too.
You need to spray weekly with a fungicide that lists fruit immediately, once fruit set and alternating with two or three types that have different active ingredients in them.
Your Certified Nursery Professional can help you with this.
Always read and follow label instructions.
Study up more on Apple culture on the Aggie Horticulture website fruit section.
Especially on weed management, proper pruning, irrigation, fertility, etc.
Texas A&M AgriLife Extension Service
County Extension Agent-Horticulture
3355 Cherry Ridge, Suite 212
San Antonio, Texas 78230