Derramando comes from the verb derramar, which means "to spill". It's a much more poetic and dramatic way to describe crying than the common verb llorar (to cry).
In the song, Selena sings "tantas lágrimas que estoy derramando" (so many tears that I am shedding). This creates a powerful image of her tears uncontrollably spilling out, showing the depth of her sadness over a lost love and a fading photo. It's a beautiful word for expressing overwhelming emotion.
This song is all about holding on to a past love through a single photograph. Selena describes a nightly ritual: "Tengo una foto de ti / Que beso cada noche antes de dormir" [I have a picture of you / that I kiss every night before sleeping]. But this isn't just a sweet memory. The photo is physically wearing out from her sadness. She says it's "media rota ya se está borrando / Por tantas lágrimas que estoy derramando" [half torn and already fading / from so many tears I'm shedding]. The very thing she's holding onto is being destroyed by her grief.
Even though it's painful, the photo also brings back happy moments. It reminds her of the exact moment they met at a party and the "tímido beso que te di" [shy kiss I gave you]. In the end, though, she keeps coming back to the hard truth. The good times are over, and all that's left of the love are these "Fotos y recuerdos" [Pictures and memories].