My driver's license was suspended for not having insurance. Should I even bother to apply for a medical? My insurance lapsed for a few days, and during that few days that I got caught.

Furthermore, it's the second suspension in my life because I got a bunch of tickets when I was younger.

I hold a sport-pilot license which would be invalidated if I was rejected for the medical.
A sport pilot license does indeed require a valid driver's license OR a minimum third-class medical certificate. If you don't have a medical certificate, you cannot exercise sport pilot privileges until your driver's license is reinstated.