I really need to recommend you speak with a tax and finance expert. But, I can give you some basic information on how forming an S corporation might impact your taxes.
Let's start with the basics: S corporations are taxed in the pass-through method. Meaning, all income is passed through to each stakeholder and taxed at his or her own income tax rate. You may be able to enjoy the benefits of business deductions, which might help your tax situation. Or it might not do anything at all to help you.
Now, let's tackle the other issue, reducing your estate taxes via forming an S corporation. Here's the theory, you would be able to gift shares of a business to your loved ones, thereby reducing the amount of the business you own which would be taxed upon your death.
As I understand it, you are a non-employee doctor who is contracted to work in an emergency room. Once you die, the purpose of your S corporation business would cease to exist. Likewise, by splitting up shares right now, each person would get a portion of your income right now.
If you want to pass money on to your loved ones but avoid the estate tax, another way to do that would be to use gifts (you can give away up to $23,000 each year without incurring a gift tax) while you are still alive.
Roth IRAs may be a good option, or using another retirement savings option for self-employed people (such as a SIMPLE plan). Whole life insurance is a great way to pass money on to your heirs without incurring the estate tax. And remember, you can give as much money as you'd like to pay someone's medical bills or to pay for education.
Disclaimer: Please understand that I can only give some basic background information on the internet. All tax matters, especially matters as complex as this, should be discussed with a qualified professional who is intimately familiar with your specific situation.