Broncas is a colloquial Spanish word for 'troubles' or 'problems'. While 'problemas' is more common, 'broncas' adds a more informal and sometimes more intense feeling to the difficulties being described.
In "Todavía Te Amo," the singer uses it to confess, "Desde antes traía broncas en el amor" (Even before, I had troubles in love). This reveals a history of romantic struggles, making his current heartache even more poignant and relatable. It's a word that adds a touch of everyday realism to the emotional lyrics.
The first half of this song is one long excuse. He opens with "No creas que me dio pa' abajo tu adiós" ("Don't think your goodbye got me down"), insists he had trouble in love before she ever left, and swears the call she got from him was an accident: "Estaba borrando la conversación / De nosotros dos" ("I was deleting the conversation between the two of us"). Nobody deletes a conversation and dials by mistake. He knows that, and so does she.
Then the chorus drops the act, and it does it with the best line here: "No estoy llorando / Traigo un 'Te extraño' en el ojo" ("I'm not crying, I've got an 'I miss you' in my eye"). The lump in his throat gets the same treatment, "Es el 'Te amo' que quiero decirte" ("It's the 'I love you' I want to say to you"), until he stops explaining himself altogether and just asks to come back to her side. Two and a half minutes is exactly how long the denial lasts.