Just curious can you easily sue a private doctor in America? I imagine it varies state by state?
There's a little variance from state to state, but it's easy to get it started. You/Your lawyer basically sends notice that you intend to sue for whatever grievance, and hope you can get a few experts in the field to agree that there was some sort of injury was caused. If you can get those second opinions in your favor, off to court you go.
The biggest thing is the Statue of limitations in America. They're all different by state, and there's even sometimes difference in the state's own law depending on circumstances. For instance California, is 1 or 3 years depending on when the injury was discovered. The shorter timeframe is for immediately knowable injury. The 3 year term for undiscovered inury.