Should I file as Head of household or continue as single? What would change if I change to head of household?

HOH gets a higher Standard Deduction and different EITC,  for example.  But you must have a qualified Dependent, and meet other requirements to be HOH.  It is generally used by Single parents with children.

Guide to Filing Taxes as Head of Household - TurboTax Tax Tips & Videos (intuit.com)

To file as Head of Household, you must have a qualifying dependent. Please see the rules and who qualifies under "Head of Household" starting on page 23 in IRS Pub 17. 

Generally, it is better from a tax point of view to file as Head of Household (if you qualify), because the Standard Deduction is higher, and the tax brackets are better.