I think you've shot yourself in the foot with your layout. You've got a high-power package, and three of your highest-current traces are long and thin.
When a switching supply IC vendor gives you a recommended layout, they mean it. Power ground, L1 and L2 are all high-current pins -- that's why the package has the unusually long stripes under there.
Note that in the recommended layout (shown below) they've maximized the area of the ground plane going to the power ground pin, and they've put vias under the chip package to get the L1 and L2 traces out to great big wide traces on the opposite side of the board.
Note, too, that they're bringing the input power out to a fill -- this is probably for thermal as well as electronic reasons.
You need to think like an electron -- and a phonon -- and make sure that there's plenty of copper for them to travel in the vicinity of that chip. If you can't follow the reasoning for their layout, then just copy it exactly.
(And the sound from the coil -- or possibly nearby caps -- is because voltages and/or currents are changing rapidly, making components bend or expand and contract. It's probably happening more than it should -- I would not be at all surprised if the deficiencies in layout were causing the circuit to oscillate, which would make any current/voltage excursions worse than normal).