Did you respond to the question of whether you had an automatic trans or manual?
I had a car once with a pinhole in the diaphragm of the transmission modulator valve.
The engine would emit horrendous clouds of white smoke whenever it got a sip of fluid.
Before a friendly mechanic clued me in to what was happening, I thought I was in for a total engine rebuild.
A new valve cost about $12 at the time, and it took 5 minutes to install. Problem solved.