Literary techniques allow writers to add interest to a story and create visual images for a reader. Readers can understand and appreciate what are universally accepted devices which ensures consistency and recognition.
Dramatic effect is used to convey details of an obvious tense situation in both "Shrieking with fear" and "My anxiety grew." Introducing a sentence with "shrieking with fear" immediately prepares the reader for the worst. There is obviously a need to emphasize feelings. The writer can aptly and convincingly convey a message this way and introduce the character who is in fact experiencing these emotions. Abstract ideas do need vivid descriptions and a mood which is an essential literary element is certainly established and a visual image created through imagery; shrieking, fear, anxiety being strong words which appeal to a person's senses.
It is not possible to associate the growing anxiety with anything without the context which may reveal the use of metaphor or simile.
In "Shrieking with fear", the most obvious tecnique used is auditory image ie; "shrieking". It is also a simple/sharp sentence, (which means it has clarity) mostly aimed at emphasising the "fear" in the phrase.
"My anxiety grew" is also a simple/short 'sentence' used to create a sense of tension and suspense in the reader's mind, therefore, it'll be attracting/persuading them to read on and find out more. In a way, it also indirectly show's the 'writer's' "desperation" to solve or get out of any situation, problem, etc...