There's no adjustment left or right that I'm aware of. Have you read through your owners manuals? I guarantee it'd be mentioned there if it exists.
Some vehicles have headlights which do rotate according to the direction of the steering wheel, but only in sight increments and I'm not sure if those could be tweaked either..i do know a failed one looks. The light will bounce around inside the housing and people driving in front of you will undoubtedly not be happy at the bobbing lamp.
If your lights aren't aligning directly then your headlights are not installed correctly. Or, perhaps the hardware is becoming loose that bolt the housings in place . I've seen that too where the headlight might shift sightly left or right as a result. You can usually check by placing your hand on the headlights and push it in and try to pull it out. See if there's some wiggle. There shouldn't be.
Lots of places are selling aftermarket h11 bulbs that are not actually h11, but instead are mounted upside down (but they will press into the Keyed slot just fine). Only difference is one is meant to be in fog lights so it could end up being installed upside down. The light projecting from the headlight would look off probably.