Yes it is true that the transaction fee matters. The fee is to pay miners for space in a block that they create. They don't care about the value of the transaction, it means nothing to them. All they care about is the size of the transaction and the fee it pays. Typically transactions are selected by their fee rate, the satoshis/byte paid by the transaction.
Your options are to wait for it to confirm, wait for the network to "forget" about the transaction, attempt an RBF double spend transaction, or ask a miner to help you.
For the fourth option, you can contact the users
Quickseller and
macbook-air. You can also try using
https://www.viabtc.com/tools/txaccelerator/ to "accelerate" your transaction.