Seems like that voicemail icon is being persistent! This may sound silly, but try powering down your phone completely and see what happens once you turn it on again. I'm with Roger's as well, and restarts usually took away that icon. Powering down your device may take away any bugs that are there.
Another suggestion is to boot your phone into Safe Mode. It may or may not help matters but it's a shot! If the icon does go away then there is an app that is interfering with things.
One thought: do you use Facebook Messenger to make calls and such? Do you have it integrated with your SMS app? What about Skype? Anything that involves calling/video chatting? Maybe open up those applications and see what happens. Again, it's a long shot but you never know!