Handling fear and self-doubt, for me, come down to understanding what these really are in moments I feel them.
Fear should be a useful and intelligent emotion that results in safety and remaining alive and well. It may not be a pleasant feeling in the moment, but it is valuable and a signal not to be ignored. Over time, wisdom and experience helps refine fear into a sharp tool of benefit we thoughtfully listen to.
Self-doubt is a finicky emotion, often masquerading as other deeper emotions or histories needing further contemplation. When I doubt myself, I try to examine it and peel back a layer to see what is underneath the lack of confidence in myself. Is it having to untangle a long history of being made to believe I was wrong when I really right? Is it a deeper experience that long ago made me lose faith in myself? Or could it be an easy avoidance to doing the next right thing?
Mainly, handling emotions like these come down to understanding the feelings and seeing them for what they are / are not, instead of drowning in an ocean of anxiety and overwhelm.

