What is this notification icon that looks like a raindrop?
I would start by looking at the list of currently running apps in Settings -> Apps  -> Running (could be different on Sony's devices.)

Narrow the list down by ignoring Google's and Sony's own services (e.g. Google Play serviced, Google Search, Google Keyboard, etc.)  Now examine each app that you don't recognize by taping on it, and tapping the "Stop" button.  If the icon on top disappears - that's the app which was spawning it.  You should now be able to open the app, go into its settings and look for a way to disable the notification icon.

If you are still unable to find the app after going through all 3rd-party apps, it's probably one of the system apps belonging to Sony.