You must have a qualifying dependent to claim HOH.
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
Provide some details about your "working taxpaying" child. How old was your child at the end of 2021? Was he a full-time student in 2021? We need more information.
Most of the time, a child working does not interfere with you claiming them as a dependent. You must consider all the usual rules.
Your child is your dependent and a qualifying person for HOH if,
When kids go to college, they are usually still considered to "live at home" since college is considered a temporary absence. And they usually don't provide more than half their own support, although this can get complicated if they have large student loans in their own name, since student loans in their own name count as support they provide themselves. Also, a child's income is only support if they use it for their living expenses; if a child is saving their earnings, or using their earnings to support someone else (a partner or child, for example) then they are not providing support to themself.