Will I be allowed to enter Shanghai within 72 hours free visa in my case or need to apply for one?

Sorry, you can't. The place of departure shouldn't be the same as your destination.

Thanks, Amanda! And what if I take flight from USA to Shanghai will not go out and will continue to Hong Kong and on my way back from Hong Kong to USA will stay 2 days in Shanghai and then will go to USA? Will it work?

If you fly from the USA to HK and stop over in Shanghai, then it won't be a problem. You needn't stay at the airport. You can enjoy 72 hours free transit as you land at the Shanghai airport.

Of course, your arrangement is OK. I mean "flying over Shanghai to HK and don't leave the airport".