What could these feelings be, and is there a way I can overcome them to make my life easier?

Every time I interact with certain people or I do something for someone, I always get this feeling that can be described as some sort of anxiety and/or fear of making mistakes or fearing that somebody may be dissatisfied with my work or something I've done for them, especially if I do end up making a mistake. Maybe it's a lack of self-confidence? It's strange because a part of me knows that I'm doing a good job and that I have nothing to worry about, but another part of me feels otherwise.

What do you think I should do?