If you write or design, you must believe in what you do. If you don’t believe you have something to express, there are plenty of other jobs out there. If you believe in what you do, and if you’re doing it for real, you must find ways to let people know about it.
There is a difference between being arrogant about yourself as a person and being confident that your work has some value. The first is unattractive, the second is healthy and natural. Some people respond to the one as if it were the other. Don’t confuse them. Marketing is not bragging, and touting one’s wares is not evil. The baker in the medieval town square must holler “fresh rolls” if he hopes to feed the townfolk.