Will God punish me for telling my friend's mother about her relationship with an older man, after she caused a rift between us and cursed me?

Dealing with the reprehensible mixing that resulted in someone becoming attached to you, and then your friend becoming attached to him, necessitates repentance to Allah. You should have advised your friend kindly and explained the impermissibility of her conversations with the person, instead of exposing her and informing her mother. You erred by not advising and by revealing what was concealed, and it seems your intention was to triumph for yourself, not to prevent evil. You must now advise your friend and call her to sincere repentance, out of fear for her from Allah's punishment and out of love for good for her. Your repentance for what happened will, by Allah's permission, erase the sin.