Corriente literally means "current" (as in a flow of water or air). It's an interesting word because it can also mean "common" or "ordinary" depending on the context.
In this song, DELAOSSA uses it in the phrase "nadar contra la corriente" (to swim against the current). This idiom means to go against the popular opinion or the established way of doing things, highlighting the struggle and independence of the artist.
DELAOSSA, DANI, and Kiddo's "No Te Necesito" is a super relatable track about moving on from a past relationship, even when it's still a little tough. The singer is out there living his life, focused on his career with "el estudio, los viaje', el estrés de la gira" [the studio, the trips, the stress of the tour]. He's trying to ignore messages and missed calls because that's "el precio a pagar de esta vida" [the price to pay for this life].
But even with all that focus, he admits, "Si llego al hotel siempre me acuerdo de ti" [If I get to the hotel I always remember you]. He knows he's better off without her, saying "Aunque sepa que no te necesito" [Even though I know I don't need you] and "Aunque sienta que estoy mejor sin ti" [Even though I feel like I'm better without you]. Still, he remembers when her kisses "valían más que los exceso', que la fama y que los peso' pa' mí" [were worth more than the excesses, than the fame and than the money to me]. It's a really honest look at how you can be doing great on your own, but still have those moments where you miss what you had.