I'm so sorry to be reading this shibamom. I know we like to say that pets are for life, but sometimes life throws us hard curveballs and hard decisions have to be made.
If I was in your position i too would consider rehoming....but perhaps we can offer some help/advice.
Perhaps there a few things that could be done that might still be able to help you. The first thing that comes to my mind is desensitization. I might try to record your child's voice and play it at a reduced volume during something the dog likes (perhaps a walk). Gradually I'd increase the volume to where it matches your son's voice. This might get the dog to become desensitized to the wailing and outbursts.
I'd be very curious to hear what other members advise as we have some very experienced and smart members.
If nothing worked and I did need to rehome the dog...the best candidates might be people that already know the dog. Gradual visits to their home would be my preference along with bringing a tshirt with the smell of any new potential owner.
This is so hard - I'm so sorry for your situation
and I hope some members may have additional suggestions or insight.