IRS changed refund amount

Hi, 

I am an international student (F-1 visa) and resident alien for tax purpose starting from 2021. I have spouse (F-2) and a child (4years, US citizen). While filing my 2021 tax return as 'married filling jointly', I also applied ITIN for my spouse and received it after 10 weeks of filing. My spouse has no earning.

 

I filed my 2021 tax using turbotax and claimed child tax credit, recovery rebate credit and earned income credit. I got a letter form IRS stating that they denied my EIC. They said:

" We didn't allow the amount claimed as Earned Income Credit (EIC) on your tax return. The individual taxpayer identification number you gave us for yourself and/or spouse was issued by the internal Revenue Service and does not qualify you for the credit."

 

It is evident that for including my spouse (having ITIN) I did not get EIC. 

 

My question is: should I file my tax next year as 'head of the family', so that I can qualify for the EIC? Does filing as 'head of the family'  overall decrease my tax refund even if I get EIC?