Laurynlmiller You can sell albums, sure, but there's no Write Song interaction. I think the text for that promotion says this?
Time to work your star image. There’s a brand new stage outfit, and with your original songs and four Sing-A-Grams recorded, you can now sell your album for exposure and Simoleons!
It's worded poorly, but I would guess what it's trying to say is that your sim has written a couple new songs and released an album, not that you can have your sim write songs. It's like saying that your sim in the medical profession is going to or has graduated from medical school—it doesn't happen on-camera, so to speak; you're just supposed to understand that it did.