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I have not been able to identify this infestation. It would not appear to be a fungus, most likely insect infestation of some kind (since they come off) I would treat this with Neem Oil as it does work as both a fungicide and insecticide.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
https://www.gardeningknowhow.com/edible/fruits/peach/common-peach-diseases.htm

There are 2 things that it might be. The first is that it may be brown rot. This will rot the fruit on the tree and cause it to shrivel up. Here is more information on that:
https://www.gardeningknowhow.com/edible/fruits/peach/brown-rot-fungus.htm

The other is the flowers are not being properly pollinated. Improperly or under pollinated fruit will be aborted by the tree early on and can simply just shrivel on the tree. This article will help with attracting pollinators to help with getting the tree pollinated:
https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm

Deep infrequent waterings are more beneficial than frequent shallow watering.

The surface soil should dry between waterings.

This could be peach borers. They can attack either the branches or the fruit. This article will help if you have not read it: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

This article should help: https://www.gardeningknowhow.com/edible/fruits/peach/tree-with-no-peaches.htm

A few things could cause this. First, it could be a chilling issue. If a peach tree gets just a little bit too little chilling in the winter, it will button the fruit, which means that it tries to grow them, but they will be deformed, stunted or fail to mature. Since no one really had a cold winter this year, it is likely that chilling could be a factor. Here is more info: https://www.gardeningknowhow.com/edible/fruits/peach/peach-chill-hours.htm

Peach trees need to be thinned well to produce fruit. If your tree is at least 3 years old and it carries the small, immature fruit throughout the season, that may be your problem. This article will help: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm

Another possibility is that there is a problem with pollination. If this is the case though, the tree will drop the fruit in late spring or early summer. If you suspect a pollination problem, these articles will help:
https://www.gardeningknowhow.com/ornamental/trees/teak/insect-pollination-process.htm
https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm