Yes, take her to get her hearing checked, then when that is ruled out, stop shouting over her! If it is a competition who can demand attention most loudly, she will always win!
If she breaks into a conversation to tell you something of her own, say something like "Keep that in your head for a moment! How long can you remember it? Until we have finished this bit that we are saying? Then we will ask you about it and hear all about it properly. Put your hand over your mouth to keep it in! OK?"
You could even look at a watch and note the time, so that you can tell her how long she kepther news inside, and make a game of it. Continue to talk to one another for a sentence or two - briefly, she won't be able to keep it in for long! - and then be sure to ask her about what she was going to say.
This won't be cured overnight! She is the centre of her world, and won't realise that other people have lives until she has had a bit more practice at playing second fiddle.
The daughter of a friend of mine years ago had it down to a fine art - she would sit on her mother's lap, facing towards her, so that her head was always between mother and me and she was gazing into mother's eyes from a few inches away. When mother moved her head to the side to talk to me, daughter's head would move too to cut off the view. It was like a chess game, at checkmate. Her mother never seemed to notice, just kept dodging from side to side like a ski slalom course.