Right next to the East Pools TP, you normally have to beat an arena in order to progress in Pools. You even need to do it twice: once without water dash and another time when you get water dash.
It's actually possible to skip that arena. Since it will only trigger if you are standing on the wooden platform, you can swim underneath it and go to the left side of the arena without starting the fight. In most cases, the door should be opened but it can happen that the door is already closed. If it's the case, you can either die on the spikes above the door or reloading your savefile in order to open it (you may have to do it multiple time before it works). Once you passed the door, you can continue in Pools like normal.