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I have found the following examples in <http://tatoeba.org/jpn/>

> 頭{あたま}が混乱{こんらん}している。I'm confused.
>
> 本当{ほんとう}に参{まい}りましたね。I'm really confused.

Are these examples a natural way to deliver the idea of being confused?
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2017-04-21T00:57:13.603
46734
2018-08-02T00:50:16.787
2020-06-17T08:18:27.500
-1
3371
question
translation word-requests idioms
How to say "I am confused"?
混乱 is the proper word to express confusion.  
So your first sentence is good.  
There could be a few other ways to express confusion but I am not sure I would
consider the second sentence one of them unless used in a very specific
way/situation.

参りました or the casual 参った means you have lost/given up etc...  
For example, I suppose you could use it to your friend after a very
complicated math class to express the fact that you didn't understand
anything. As in you have been defeated by your teacher or given up
understanding what the hell is going on in that class.
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2017-04-21T01:28:43.550
46738
2017-04-21T01:28:43.550
18142
46734
answer
There are so many ways to say "I am confused." that you might not get a very
good answer unless you explain what situation/context you have in mind.

「頭が混乱している。」 is "good" in the sense that it could not really mean anything
other than "I am confused." It could sound a little stiff if said in a casual
situation as 「混乱」 is a bit of a big word for a light kind of confusion.

「本当に参りましたね。」 would be a hit-or-miss kind of expression in that it can mean
many different things. "Troubled" or "beat" would be the most common meaning
of 「参った」, not "confused".

The "real" native-level, non-textbook expressions for "I am confused." that do
not use big Sino-loanwords would include:

・訳{わけ}が分{わ}からない

・まごついてしまう

・困{こま}ってしまう

・うろたえてしまう

Then again, you might have a situation in mind where the use of a big word is
completely appropriate.
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2017-04-21T03:11:51.687
46741
2017-04-21T03:11:51.687
46734
answer