The turning right clue might be misleading. You might just not be feeling it when going straight. The fact you don't feel it at lower speeds and when accelerating leaves out a worn cv joint housing. The common suspects are a bent wheel or a broken tire belt. Those will be felt more when putting more weight on that tire, which is what happens when turning right.
If any work was done recently that involved removing the left wheel, look for rust, scale, or other debris that got stuck between the wheel and brake rotor or between the rotor and hub. This is somewhat common when do-it-yourselfers or inexperienced mechanics remove a brake rotor and don't scrape off the round spots of rust buildup on the back side. That spot of rust can hold the rotor from sitting squarely on the hub.
If those don't seem to be the problem, your mechanic can use a dial indicator to measure the "lateral runout" of the wheel and the brake rotor to check them, and he will inspect the rest of the steering and suspension system.