I take the hard part of this question to be not "hwo can I find carriage returns in a file?" but "how can I find out which files my bashrc uses?"
For the second question, you can try something like this:
bash -x .bashrc
This will show you everything your bashrc does, including all the files it refers to. It's noisy, but should help you track down which files are being used.
Except in fact, my (and many other)
.bashrc files exit early if not run interactively, so you have to trick it into passing that check:
bash -ix .bashrc
-i forces interactive mode.
To grep out just the cases where you source a file, something like this works for me but I can't promise the regex catches everything:
bash -ix .bashrc 2> >(grep -E '^\+* (\.|source)')
I guess you might also want the error messages, so something like:
bash -ix .bashrc 2> >(grep -E -e '^\+* (\.|source)' -e 'command not found')
If for some reason none of this worked, I would resort to
strace -e open bash or something like that, to find every time any file is opened by your bash session. But that's an even more heavyweight / noisy solution.