Unfortunately fungi exhibit a lot of variation and often need microscopic analysis to get to species. The best app out there is iNaturalist, which has pretty well trained AI. But their suggestions are only the start. INat has a robust community of community scientists who will often suggest better identifications (this varies from region to region). The first step is always taking very good pictures that show all the key morphological characteristics (inc gills/pores, stipe, ring, bulb/volva, ideally spore color, discoloration/bruising/latex as well as odor and taste)
As I think, there is no available application to determine the fungi. You must isolate the fungi and prepare cultures and slides for macroscopic and microscopic tests, then you can confirm your identification with sequencing.