My favorite definition of fearlessness is this: the ability to remain soft and open, even under very difficult circumstances. Most often, fear causes us to shut down to our own and others' humanity. We just want to get away, but the quickest way out is to stay. If you can slow down a bit, you can see that fear rises, abides and dissolves on its own. Allowing this process is the mark of the spiritual warrior. The coward turns attention toward fighting fear; the warrior accommodates it.
Try this: The next time you notice fear rising, whether it appears as anxiety, melancholy, or anger, stop, grab a piece of paper, and write one short sentence that describes your fear. Start with the words "I'm afraid...," then scribble the first thoughts that come to mind, without regard for grammar or rationale. It could be something such as, "I'm afraid to check my e-mail because I've already got too much to do," or, "I'm afraid about an upcoming conversation with my boyfriend," or, "I'm afraid I have cancer." Slowly read your words over three times. Take a full inhalation and exhalation after each reading. Avoid any attempt at amping up or toning down your agitation.