so in the future I would recommend using a fee slightly higher than minimum average to make sure your transaction gets confirmed quicker even in cases of fee jumps like yesterday.
There is no need to pay higher than the required fee, unless you are in a hurry and you want to make sure that your transaction will be confirmed in the next block. Instead, I recommend using a wallet that supports RBF, so that you can easily replace your transaction with a new one paying higher fee.
Paying only the required fee is enough in most cases but since the fees are also fluctuating you can sometimes end up in a situation such as the one in the OP. I always used to pay the lowest required fee, depending on how congested the network was, and it happened multiple times for my transaction to get stuck for a much longer period of time than expected. So, just in case you want to avoid any delays and make sure you get the required confirmations within a couple of hours it does not hurt to pay a slightly higher fee. As far as I'm aware RBF only works if you are the sender, so you can't use it while withdrawing BTC from a website for example.