There are a number of self-hosted music streaming servers. Some quick googling shows Ampache, Mopidy, mStream, and Airsonic as the four biggest ones. Some of them have apps for Android/iOS, some support the Subsonic protocol which has a number of compatible mobile apps. And of course also a website interface.

Put it on an old computer / raspberry pi in a closet, or on a cloud VM. Domain name is <=$12/yr and many providers let you do DDNS via their API.