Is my breaking off the relationship with that girl—because she went too far in expressing her admiration and did not respond to my advice that attachment should be to God alone—a sin that warrants her not forgiving me in this world and the hereafter, and will my reward in my grave be halted because of that?

It appears that the love mentioned is carnal, not love for the sake of Allah. One should be gentle with the girl and help her in treatment, while minimizing interaction with her. If harm to one's religion or worldly affairs is feared, and the aforementioned methods are ineffective, then there is no harm in cutting off the relationship with her for a legitimate reason. Her not forgiving him at that point would not be a concern.