Hi Amy
As those are Web App Builder apps, not Story Map apps, it might be good to post this as a new question on this thread: Web AppBuilder for ArcGIS . I'd also recommend contacting Esri Support directly so they can walk through the issue too. I suspect this might be a security setting on the Microsoft Edge browser though, and not ArcGIS related.
I like the Edge browser but it does seem to have some peculiarities. When I work from home over our corporate VPN, it can't access the web at all, but works fine when I am off VPN.
Rupert