[間違]{ま・ちが}い[探]{さが}し is a name of game, which is called "Spot the difference" or something like that in English. This pdf is an example of 間違い探し for young children.
Using the game name 間違い探し, she mildly told that her topic and your topic were different. She didn't really wonder whether you were playing 間違い探し game. 「間違い探しでもしてらっしゃるのでしょうか?」 implies that "What you're doing, like finding differences or mistakes, is off-topic. Why don't you talk about something on-topic?" I don't know if what you talked about was really off-topic, but, she seemed to think it was off-topic.
This 「少々疲れます」 implies "No more, please."
The whole line seems to imply "we've been talking to each other, but actually not communicating with each other. It seems meaningless. I talked to you, but you've been just caring about something else. That makes me tired."