Would it be a bad idea to try to pop my pilonidal cyst?

On your own NO. Pilonidal sinus, abscess needs urgent incision and drainage by a physician, if undrained may lead severe complications like necrotizing fasicitis etc, a trained professional can help you with minimum pain, please see your physician or go to er.
Yes. See a surgeon. Pilonidal cysts can be difficult to treat and difficult to heal. An incision in the wrong place or opening in the wrong place can lead to months of poor healing. See a surgeon to have it properly evaluated and treated.