I went ahead and made a little script based upon the information provided by Snow and Catija.
Just paste this in the console when looking at your messages.
https://chat.stackoverflow.com/rooms/info/11/php/?tab=stars&filter=mymessages
Before you run it modify start room id and end room id to it encompasses the rooms you want, or modify the loop that it loops through an array of relevant room ids.
My output

+function() {
var startRoomId = 1;
var endRoomId = 20;
var textList = [];
var TextObj = function(str, stars, room) {
this.room = room;
this.text = str;
this.stars = stars;
}
for(var c=startRoomId; c < endRoomId; c++) {
$.ajax({
url: 'https://chat.stackoverflow.com/rooms/info/'+c+'/php/?tab=stars&filter=mymessages',
success: function(res) {
var $response = $(res);
var texts = $response.find('.monologue .messages .message');
var room = $response.find('#content .subheader h1').text().trim();
texts.each(function(index, domElement) {
var $el = $(domElement);
var number = parseInt($el.find('.stars.vote-count-container .times').text());
$el.find('.stars.vote-count-container .times').text('');
var obj = new TextObj($el.text().trim(), isNaN(number)?1:number, room);
if(obj.text.length > 0) {
textList.push(obj);
}
});
},
});
}
console.log(textList);
}()