a person who suffers from erotomania
Greek eros 'love'
"one driven mad by passionate love" (sometimes also used in the sense of "nymphomaniac"), 1858, from erotomania (1813, defined then as "Desperate love; sentimentalism producing morbid feelings"), from comb. form of erotic + mania.
erotomania e·ro·to·ma·ni·a (ĭ-rō'tə-mā'nē-ə, ĭ-rŏt'ə-)n. Excessive sexual desire.