Espinita is the diminutive of espina, literally meaning "little thorn". It's a beautiful and common metaphor in Spanish for a lingering pain or a bittersweet memory that you can't get rid of.
In the song, the artist sings "Serás esa espinita que jamás podré sacarme" (You'll be that little thorn that I can never remove). He uses this word to describe how the memory of his lost love remains with him, like a small, sharp object stuck in his heart. It perfectly captures that feeling of a persistent, nagging emotional wound.
Julión Álvarez y su Norteño Banda deliver a straight-up breakup gut punch with Rey Sin Reina. The singer hates being the one walking out the door ("Odio ser en esta historia la persona / Que se va pa' no volver" [I hate being the person in this story who leaves never to return]), but the relationship is completely over. He uses very direct Mexican slang to express his frustration, admitting that accepting he is not the one for her "me cala un chingo" [stings like hell / hurts a ton; from the slang un chingo, meaning a massive amount]. It will not kill him, but moving on is going to drag out forever while he replays the whole mess in his head.
His pride is battered, and he throws out some vivid, slightly dramatic self-descriptions: without her, he feels like a puzzle missing pieces, a sad clown, and literally a "rey sin reina" [king without a queen]. Even though he is furious that things failed ("No funcionó y reconocerlo da coraje" [It didn't work out and admitting it makes me angry]), he switches respectfully to the formal "you" with "Difícil olvidarla a usted" [It is hard to forget you], showing how deeply he held her in esteem even as he settles for only holding her in his dreams.