No, you cannot file Head of Household given the details of your living situation.
Yes, you will need to amend.
You also have the option of making an election to file jointly.
This would allow you to claim the higher Married Filing Jointly Standard Deduction compared to filing Married Filing Separately.
You can make the election on an amended return.
Your spouse would not qualify you to file Head of Household and if you do not live apart, that also would not qualify you.
HERE is a link with more information.
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