In a nutshell is Child pays for parent basically resending that unconfirmed transaction to myself again with higher fees?
Correct. If the original transaction has 1 input and 2 outputs, you don't even have to pay a lot in fee. Just 1000 sat or even less will probably be enough to reach the next block. You only have to get ahead of
the bulk of transactions with 1 sat/byte.
I set the fee for 1 sat /vb when receiving the transaction.
For next time: 1.1 sat/vbyte puts you ahead of the many low fee transactions.