I have been using conversation bubbles with my messages(texts) and messenger (Facebook) for quite a while now.
Hi, I am very sorry to hear you are going through this. What model phone is this happening with? Additionally, have you tried clearing cache and data from Messenger to see if that helps? I noticed on the picture provided it says bubbles are not supported for the app in question, so if that does not help, I recommend contacting the developers of Messenger.