Lower altitude flyby of Allegiant Flight 3145 on a 180 flight trajectory.

I was seated in seat 4A window seat on Allegiant Flight 3145, an Airbus 320 aircraft, that was at 34,000 feet cruise altitude at 450 knots (as related by the piloting air crew). As I glanced out the window I witnessed an oblong, cylindrical wingless object at an estimated 15-20 thousand foot altitude. This object was on a course parallel to Flight 3145 but on a 180-degree trajectory. Allegiant Flight 3145 was out of Austin-Bergstrum International Airport, Texas, with a destination of McGhee-Tyson Airport, Knoxville, Tennessee. The object was visible for an estimated ten seconds off the port side, below and disappeared aft. At the completion of my flight I spoke to one of the pilots after I identified myself with identification and asked if they had had a radar contact at this estimated altitude at 08:58 CDT during our flight. This pilot stated that the flight crew had not had a radar contact at that time. I asked if this observation was reportedable to the FAA and he stated that it was. A check of the FAA website referred me to your site after a second search. The object was completely white, cylindrical without lights and without wings. Estinated size was comparable to an airliner. Weather was scattered clouds and the object was above cloud level. My professional background is that as a paramedic with thirty-four years experience as both paid and volunteer.