Pay out of pocket or make a claim?

[eileenwithfaith]

I had an at fault accident. I fell asleep and caused damage to my rear tail light and car body. I’m getting estimates at $1800-$3200 for the repair. Is it better to just pay a out of pocket on my older car 2005, 160k miles, but in good overall shape besides the ding? I’m on my parent’s plan and would feel bad having their insurance increase based on me.

pictures of damage