@Anonymous , generally as a non-resident alien ( whether you are present in USA or in your own country ), US taxes you ONLY on US sourced / connected income.   For US citizen/Resident/ Resident for tax purposes , one is taxed on world income.

As a resident in foreign country , taxation  of income from US would come under the purview of any existing tax treaty between US and that "other " country.

Thus , in your particular case  , while 1099-misc probably is not valid in your country, it is proof that you were paid a certain amount from  US sources and thus us subject to US taxes -- you should look at the  tax treaty between US and your country  of residence  and/or citizenship.

Absent, any other local income during that 1099-misc period, you could simplify the  whole process by filing a US tax resident return on form 1040 covering the whole year -- the risk here is that you would be exposing  your world income to US taxes.

The correct procedure is to file a form 1040-NR  ( not supported by TurboTax -- use Sprintax  or similar )  for the earlier period and then file a form 1040 ( supported by TurboTax )  covering the H-1B period i.e the rest of the year.  You are essentially in a Dual Status situation.

Depending on when you entered he country, any earlier stays in the country for any purposes etc. , the whole position may change .  It may behoove you to see a tax professional familiar with international filing .  

If you need  help here please provide . your country of residence / citizenship where the earlier work was done, dates associated with this entry into USA, dates and number days present in the USA during years 2017, 2018 and 2019

You will need to file as a full year resident if you were considered a US tax resident in 2018.  

You will file as self-employed for the first 3 months of 2019.  You can use the self-employed edition of TurboTax.  You will enter the income your earned for the 3 months and then claim any business expenses to help offset the business income.  If you have no business expenses to claim you can use the Deluxe version.

You will also have to pay self-employment taxes on this income.

If you paid any taxes on China on this income, you can claim a foreign tax credit to help offset double taxation on this income.  This is only to help offset income tax not self-employment tax.

On your 2018 US resident return, you should also have included your US self-employment income.

@Anonymous  while I generally agree with  @KarenJ2  but I would like you still to consider  the following:

(a) if when you left the USA in 09/01/2018, your visa was terminated AND you had no intention of returning  i.e. you actually became a  Non-Resident Alien   ( 2018 being a dual status  taxpayer status for you ),  then that you were a resident alien for tax purposes status was terminated and invalid to consider.

(b) if however, your current employer had applied for H-1B request for you before you left for China and you were in wait period, then  @KarenJ2  is correct and you have to consider the Resident Alien for Tax purposes to have  continued and you file as  she is suggesting .

(c) if above (a) is true then your 2019 status is a dual status i.e. self-employment income in China is not subject to US taxes, just Chinese  taxes.  Your actual  start date is  03/01/2019 and thus your 2019 return is s short year ( 10 months ?)

IMHO