In a nutshell is Child pays for parent basically resending that unconfirmed transaction to myself again with higher fees?
Quite, the underlying method is spend the output of an unconfirmed transaction; it doesn't matter where you'll send it.
The original transaction isn't "
resent" but "
spent".
And now that I've mentioned it, you can basically CPFP it in Electrum in your next transaction by selecting that stuck transaction's output using "
coin control".
Just enable "
Coins" tab (
View->Show Coins), select that transaction's output or more if it's not enough for your transaction (
CTRL+LeftClick to multi-select).
Right-click to open the menu and choose "
Spend"; when you go to the spend tab, those coins will be used.
Just set the fee rate higher than the recommended to bump the parent transaction.