So, first, stop using Input.GetMouseButtonDown(0), use Input.GetButton("Fire1"). This allows your player to remap the controls. It won't fix your problem, but this is still something you should do.
Onto your problem, you have a few options:
- When the UI is up, set some global variable (eg.
gamePaused) that when true, your game logic doesn't execute. This includes shooting. - Ask the event system:
EventSystemManager.currentSystem.IsPointerOverEventSystemObject() - Check if your mouse is in a region of the screen (eg. over/not over the UI) and if over the UI, don't fire.