I was replying a message with question with an example about what I think she
was wrong and she replied this:

間違い探しでもしてらっしゃるのでしょうか？少々疲れます。

Does it sound like I asked to much in the reply, or offended her, or annoyed
her? Does she mean she was tired of answering me?

Or she means she had written the previous message wrong since she was tired?
(But she didn't use past tense with 疲れます)
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meaning
What does 少々疲れます mean in this case?
I would say she's pretty irked. The super polite language like 〜らっしゃる in
particular makes it sound pointed to me (though if she happens to always speak
like that I guess it might be okay, but I'd doubt that).

少々疲れます means "I'm starting to get a little tired/exhausted.", with the
conversation (which she called "間違い探し") being the implied cause/reason.
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[間違]{ま・ちが}い[探]{さが}し is a name of game, which is called "[Spot the
difference](https://en.wikipedia.org/wiki/Spot_the_difference)" or something
like that in English. [This pdf](http://happylilac.net/machi-
kodomonohiparty-02.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."
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