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Note that in "real" code, you'd just use std::list rather than coding up your own linked list.

You should also verify that the behavior is correct with regards to capitalization. There are several...

Note that the operators will not work for comparing two char arrays, AKA "C-style strings". In that case you'd need to use the functions in <cstring>. C++ string classes such as std::string exist...

What makes you think you can't use the <, >, etc operators? Assuming those "string" parameters are std::strings and not some homegrown variety, the operators should work fine.
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