Just trying to visualize your situation....did you start the turn to the left of the cars (on the inside of the curve)? Maybe I'm doing it wrong but when making left-hand turns while in the turning lane I usually ride the outside of the curve to avoid somebody squeezing me like you described. that way I'm right back riding along the curb on the right. The only thing I then need to worry about is somebody making an immediate right after negotiating the left hand turn.
Either way it's not the best situation because people are often times not paying attention.