From two miles away from a 16-20 kiloton explosion like Hiroshima, you wouldn't be toast instantly. Most of the nasty radiation and thermal damage from a nuke that size happens within the first mile. Getting near the wall wouldn't help so much, because the bomb is actually detonated  at 2-3000 feet or higher---it's essentially right above you, even 2 miles away. You might be temporarily blinded by the initial flash or suffer flash burns, but that would probably scare you enough to come to the surface. Now, when the blast wave hit you 10 seconds later, you run the risk of taking a car or a house to the forehead.  Plus, the most horrific injuries from atomic bombs are caused by the blast wave ripping already-blistered-and-burnt skin from your body. So, if you lived at that range, it might not be very pleasant.

Now, if your pool was within a quarter mile of the blast, you can hang it up. In the first 1/10th of a second, the air temperature would rise to around 1400F or a bit higher. Your pool with turn into steam instantly, you would get hit with that heat, a 5psi blast wave, and a high enough dose of radiation to kill you instantly without the heat and blast.