Peste literally translates to "stench" or "plague". It's a very strong word used to describe an overwhelming, foul smell or a devastating disease.
In this song, Romeo Santos uses it in a deeply poetic way, singing "Nuestro apartamento tiene una peste a agonía" (Our apartment has a stench of agony). He's not describing a literal smell, but rather the suffocating atmosphere of despair and heartbreak that now fills his home. This dramatic metaphor makes it an incredibly powerful and memorable word.
Ever been so heartbroken you start talking to your phone for help? That's exactly where Romeo Santos is in this song. He's using his phone's virtual assistant as a therapist and a messenger to try and get his ex back. He literally asks her, "Siri, llámala y dile que, que vuelva" [Siri, call her and tell her to come back]. He feels totally lost without his partner, saying his house has turned into a jungle and that he's so lonely he's "recuperé la virginidad / Haciendo el amor con la soledad" [recovered my virginity / making love with loneliness].
His whole world has fallen apart. He can't sleep, his apartment "tiene una peste a agonía" [has a stench of agony], and he's driving his computer crazy by googling her. He even feels like he's gone viral online from begging for her to return. It's a classic, dramatic bachata story of heartbreak, but with a very modern twist. Instead of writing a letter, he's asking Siri to make the call for him.