I serve my family by giving them massages. I entertain them. I finance them. I'm the only looker after of my family. What is a suitable word in place of the expression in bold?
It's not entirely clear what you mean by look after. Going by your example sentence, I suspect you mean provider or breadwinner.
1 A person or thing that provides something.
‘a leading provider of personal financial services’
1.1 A person who earns money to support their family.
‘he didn't like the thought of Dad being the sole provider for the family again’
A person who earns money to support their family, typically the sole one.
‘when Roland's grant ran out, Val became the breadwinner’
A family member or paid helper who regularly looks after a child or a sick, elderly, or disabled person.
However, the OP's coinage of *"looker after" would be perfect, if only it were a set phrase or idiom.