If you want your child to come to USA, most certainly wife is not needed to travel, I think you are capable of taking care of your own child, if it is the expense for the child while you work, and you have no other family certainly would be best for the child to stay in the country with your wife, as millions of babies are born and survive in Egypt.
With the surgery it all depends on the depth and complexity of the surgery, I had surgery on my dominant side, to fix a rotator cuff, and a torn labrum. My husband might have been here but was working a lot, and I was left to my own devices and had no issues.
I know that you want your family here as soon as possible and the waiting game is hard, I am not trying to dimmish what you experience, but we will only know what we are capable of when we are forced to go at it alone.