Well, when going faster, you don't turn the wheel much anyways....Right?...So maybe the problem is there all the time.

Jack it up by the lower control arms so the weight is still on the suspension like if it was sitting with the tires on the ground....then crank it back and forth while you look for problem.....You can steer the front wheels by hand if the ignition is unlocked and it is jacked up just by grabbing a tire on each side and push/pulling it back n forth....the steering wheel should spin and the tire should go full to each stop.

If that don't help, disconnect things and try again till you eliminate all but the offending part.