Story was read approx 15 years ago, but I feel it was older. Maybe Seventies or Eighties. Short story in paperback. 99% sure it was by Robert Silverberg. Human woman falls in love with snake-like/reptilian male alien. Alien leaves woman for another alien. He just wanted her for sex. Cue heartbreak.
Thesme and the Ghayrog is the Silverberg story. Novelette, 1982. It appeared in Majipoor Chronicles.
Thesme leaves her city and family to live in the wilderness, alone. She encounters a Ghayrog with a broken leg, and he moves into her hut to recuperate. Eventually, they have sex.
At one point, they visit her hometown, where Thesme supposes that everyone is shocked by her alien lover.
Thesme feels that Vismaan does not return her love, so after he heals, she suggests that he should leave.
Thesme regrets losing Vismaan, and searches the jungle for, and eventually finds, Vismaan and his mate, Turnome. They show her the basket of their eggs (also, they're mammals, and nurse their young) and Thesme flees.
The two Ghayrogs discuss the situation, and Vismaan returns to the hut and apologizes for hurting Thesme's feelings, saying he is 'extremely fond' of her.