You changed your fit and your average speed increased. This generally means that your muscles are now working together a bit differently than in the past. It's logical that your pain is caused by overuse of some previously seldom used muscles, causing inflammation and pressure on the sciatic nerve. This would leads to pain like what you've described.

A very similar thing happened to me when doing a hard, though flat century on a new bike with slightly different geometry (lots of headwind, stayed in the drops for long periods, always pulled my wife). The answer for me was to ice the lower back after any of these rides and to do a few simple stretches if I felt the pain returning (stand, hands on hips and lean back as far as comfortable, hold for a few seconds, repeat a few times).

You probably just need to ice your lower back for the next few long rides until your new muscles get into shape. I'd try that first before running to the doctor.