Anestesiado literally means "anesthetized" or "numbed". It's a striking and somewhat unusual word to find in a song about heartbreak, making it particularly memorable.
In "Corazón Anestesiado", Milly Quezada uses this word to express the profound pain of feeling as though her heart has been completely numbed by a past love. She sings, "Como si tuviera el corazón anestesiado" (As if I had an anesthetized heart), conveying a sense of emotional detachment and disbelief that someone could treat her as if she were indifferent to such deep sorrow.
Milly Quezada's "Corazón Anestesiado" is a powerful song about the sting of a breakup, told from the perspective of someone who feels deeply hurt and betrayed. The singer is furious at her ex-partner's insensitivity, especially when they act as if her pain doesn't matter. She sings, "No existe una canción lo suficientemente triste que pueda describir todo ese daño que me hiciste" [There isn't a sad enough song to describe all the damage you did to me], showing just how profound the hurt is.
What really gets to her is the ex's nerve! They tell her they wish her the best, even when she's on her knees, heartbroken. She can't believe they have the "cara" [nerve] to talk to her like she has an "corazón anestesiado" [anesthetized heart], as if she's indifferent to the pain and doesn't care that they've condemned their love to hell. It's a blunt and emotional look at feeling dismissed and invalidated after giving so much love.