Regardless of any billing add-on, your ability to get coverage abroad (which calls, texts & mobile data rely on) is dependent on roaming being activated - which allows your phone to connect to foreign networks.
Have you used your phone abroad previously, did you receive a welcome text message on first arrival abroad? These are good evidence of roaming being enabled if so. In these cases, manually cycling through all available local networks often resolves issues - toggling flight mode can have the same effect. You mention trying "everything" but being specific would be more useful.
You did the right thing in contacting EE-CS from another phone to report this. Presumably they enabled roaming remotely, and advised you of this. Did you try a manual network search whilst on the phone to the agent? Were you able to connect to another local network?
And if not... what did the agent advise when you told them of this?
