Inquietud tiene la connotación de a concern y ansiedad es anxiety, se refiere más a la condición psiquiátrica.

Ansiedad is more used for mental state and Inquieto ir more for the physical showing of that state. Example: '"Estas ansioso por ver a tu artista favorita" Here maybe you are not showing any moves or expressions, maybe you are just sit waiting for the artist to come out but you do feel like an explosion inside of you and happiness on your mind. If you are INQUIETA at the show means you are moving and jumping and standing up and sitting down, rubbing your hands and talking and stretching, etc. You can see when someone is inquieto but not always when some is ansioso. You can have ANSIEDAD without being INQUIETO and you can be INQUIETO not necessarily for having ANSIEDAD, maybe cause of the nerves or cause you are ust bored, etc.

Fastidio se usa para cuando nos sentimos molestos por algo, se dice así " Qué fastitio ! Viene del verbo Fastidiar, que es molestar, quebrar algo que se encontraba en buen estado inicial.

Aunque Camilo tiene razón, se puede decir "Estoy ansioso", "Estoy inquieto",sin tener una explicación con carácter psiquiátrico, es simplemente un estado de ánimo.

Camilo did a very good job answering it