"Sintigo" is about that maddening on-again, off-again feeling where you want someone gone and right next to you at the same time. The chorus says it plainly: "Yo quiero que te vayas, pero quédate aquí" (I want you to leave, but stay here). It is a contradiction, and the song knows it.
The title is a made-up word. Spanish says sin ti (without you) and contigo (with you), and sintigo mashes them together, so "Mi vida sintigo no tiene sentido" means "my life without you makes no sense". It is wrong on purpose, and it sounds like how people actually talk when they are a bit lovesick. There is a lovely sulky line too: "Me dañaste hasta la playa" (You even ruined the beach for me), followed by "Pero no es igual sin ti" (But it's not the same without you).
The fight barely matters to her: "¿Por qué fue que peleamos? Bebé, ya me olvidé" (Why did we fight? Baby, I already forgot). Her hope is simple, "Que esto no termine como termina el verano" (That this doesn't end the way summer ends). And the image that sums them up is "Lluvia con sol" (rain with sun), two things that should not go together but somehow do.