Doliente is a poetic adjective that means 'painful', 'aching', or even 'grieving'. It's more profound than the common word for painful, doloroso, as it implies a deep, ongoing state of suffering.
In the song, the artist describes love itself as muy doliente (very painful/aching). He uses this powerful word to capture the intense and persistent emotional pain of heartbreak, making you feel the depth of his sorrow.
This song is a direct and desperate plea from someone whose world has completely fallen apart after a breakup. He's not being subtle at all. He opens by asking, "Dime por qué, por qué no estás junto a mí" [Tell me why, why you aren't next to me], and he needs an answer because he feels like he's not the same person anymore. The lyrics get really dramatic, saying his heart "se partió en dos" [broke in two] and he feels like he's in "un gran hoyo" [a big hole].
He blames his ex for everything that's gone wrong since she left. He sings, "Por tu culpa me enfermé / Cambié mi forma de ser" [Because of you I got sick / I changed my way of being]. He's even started drinking to try and forget the memories, but admits it's "Difícil en borrarlo" [Hard to erase it]. The song paints a picture of total darkness without her, comparing her to the moon that used to light up his nights, which are now just "pura oscuridad" [pure darkness].