I am confused regarding entry points

Theresa, you cannot be eligible for visa free transit if you fly New York - Shanghai - New York. This is just a round trip and not a transit, i.e. here we miss a third country. To be eligible, you need to introduce a third country. This is just a sample:

New York (US) - Toronto (Canada) - Shanghai (China) - New York (US)

As you can see, like this we have fulfilled the crucial requirement of visa free transit policy and that is that immediate places before and after a Chinese destination have to be in two different countries. In your itinerary, you have the same country before and after, but in the sample itinerary that I have mentioned, you have US and Canada as immediate countries.

So, just play a bit, be creative and find a suitable itinerary that will allow you your 144 hour visa free transit stay in Shanghai.