Hello and welcome to JustAnswer!
It sounds like you've described a noisy wheel bearing. A noisy wheel bearing in the front while make a growling or humming noise that normally gets worse with higher vehicle speeds. When it's making the noise and you turn and it gets worse it's because you are loading the bearing that is making noise. Turning side to side puts more load on one bearing and decreases the load on the other, which causes the noise to change or come and go.
They're going to need to drive it to listen to the noise and determine where it's coming from. In some cases a tech will also opt to run the vehicle on the hoist while using a stethoscope to listen to the bearings as they are spinning.
If you have the necessary tools to replace a wheel bearing and are comfortable with doing the repair then it's something you could do yourself.