"Emergency Calls only" is usually a phone's indication that the home network is unavailable (most likely a local coverage issue) but an alternative one is.
"Phone network is very slow" would suggest to me, that you have a network connection but there is heavy data load locally - which contradicts the local coverage outage.
Testing your phone in alternative locations and/or comparing service with other EE users locally, would confirm/deny the local coverage theory and assist with the status checks
