If it's the data side that got damaged, you might be able to restore the disk, as long as the damage is not major. The actual data is written on a thin film that's sandwiched between two layers of plastic. The plastic on the outside can be ground down and polished back to a smooth, clean finish. Disk polishers used to be kinda popular back in the day.
It's the sense of loss, an item you enjoy that's survived all this time. I've been there, I'm sorry that happened, so we all learn, what's a better cleaning agent for CDs? I'd probably try the type of Windex with vinegar in it, but now I'm questioning that!
it depends what CD, but its a roll of the dice to use isopropyl alcohol.
I used it to get the "Blockbuster (Do not remove)" sticker off a ps1 game that i bought at a retro game store. It covered the entire disc. I thought I was going to ruin it. but I decided I had no choice as it was getting caught in my PS2 and would potentially break both if I left it alone.
It worked out, but it was a scary and calculated risk.
I bought some old vynils, one being the wall z which is a mainly white cover, so it had some stains. A micro fiber cloth lightly damped with vinegar made that cardboard cover look like new