Crazy drivers in Houston is this norm?

I moved here recently and I have noticed 4th time now a person who is in a clearly marked Left Turn Only lane to my left suddenly accelerate and barely clears me as I am turning left and he is going straight. You know those lanes next to Interstates where one far left lane is to make a U turn, the lane to the right of that is a left turn only lane and it's used to get folks onto the intersected street and the lane to the right of that is the go straight or turn left lane. I was in the go straight and turn left with my signal on the dude was in the Left Only lane and he cut me off to go straight. It would be ok if it was the only time it happened but this is like the 4th time in 2 months.