You have to define the tooltip as a child element of the inputText control. Just placing it next to the control won't work. Also (at least in RichFaces 3), tooltips only work on input controls, not on general objects such as panels (although that's not your problem).
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.