Hi Albert,
Your app is created with the ArcGIS Online Web App Builder rather than one of the Story Map apps and so doesn't get listed in My Stories, which just lists your Story Map apps hosted in ArcGIS Online. But the issue is the same: If your app prompts your end-users to sign-in, then either the app isn't shared publicly, or the web map(s) it uses aren't shared publlcly, or they contain data that is not shared publicly or which is subscription based (see this blog post for how to include subscription based content in your app). Another reason an ArcGIS Online app may immediately prompt end-users to sign in is if the ArcGIS Online account that it belongs to has expired, or, with ArcGIS Online Organizational accounts, if anonymous access to content on that Organization has been turned off in the Organization settings.
Rupert