Text written in browser

Contacted service provider said not their issue with security. Appear to have security issue with iPhone, has anyone experienced this? Having messages written in browser. Please see attached pictures as example, appears something/someone has access to phone, concerned someone is using IP address etc. Also had similar issue with prior phone where messages were being written in text message but did not type message not a case where phone is unlocked and by accident hitting buttons. These are actual conversations written. Appears to be security issue, any help would be appreciated, Thanks!