"Is it possible to have localised sea level rise?"
measure the pool level right next to your hand when you first push down, and the level in the far corner at the same time.
A more exaggerated example is a tsunami.
What is the height change in the sea in the immediate locality compared to the level when the wave hits on the other side of the globe.?
It is dissipated over a large area so it is felt more locally.
