Ilusionarme comes from the verb ilusionar, which means to excite or to fill with hope. When used reflexively, as ilusionarme, it means to get one's hopes up or to become excited about something or someone.
In the context of "No Te Olvido Mami," the singer expresses a reluctance to ilusionarme (get his hopes up) because he is already committed or has been hurt before. It's a poignant word that captures the emotional caution one might feel when faced with new love after past experiences.
Luis Segura's "No Te Olvido Mami" featuring Alexandra tells a story of unexpected love and the pain of a complicated situation. The singer expresses gratitude to his father for making him part of a legacy, then introduces a young woman who "te habría robado" [would have stolen you]. He never expected to fall in love, saying "yo nunca pensé ilusionarme" [I never thought I'd get my hopes up].
Now, deeply in love, he's facing heartbreak because he's already committed to someone else: "ahora que estoy queriendo tanto sufrir mucho porque soy comprometida" [now that I'm loving so much, I suffer a lot because I am committed]. Despite this, he can't forget her, repeating "no te olvido" [I don't forget you]. He doesn't want her to suffer or cry, even though their love might be lost. It's a bittersweet plea to remember him, even if they have to part ways.