Is the search string a single long string over multiple lines which you want to find in exactly that order? grep -f and friends generally read a file of search expressions, one per line.

Are the email messages one per file, or is this a single file containing multiple messages? The .eml extension is not well standardized; it could be either.

If you have one message per file, grep -l searchstring *.eml will list the ones which match, but again, that's assuming the search string is shorter than maximum one line.

You really could take the time to think of a thread topic which would identify this thread among the others; basically, everyone who posts here wants help, some urgently.