Hi JB,
It's a little hard to tell based on your post, but I'll take a stab.
First, you may be running into mixed content issues. I see you've added your service to ArcGIS.com using https, but are you also accessing your web map/web app using https? If you're using http, I can see the browser complaining.
You can confirm by opening up a new web map and pressing F12 on your keyboard to open the browsers DEV tools and clicking on the console view to look at any errors generated. Hopefully that tells you the issue.
To be clear - you're able to add your service as an item to ArcGIS.com, but you're unable to add it to a web map, is that correct?
Also, is the resource you're adding secured - like does it require username/password to access?
~Randall