"anxious and concerned" is correct and usable in written English.
You can use it when you are talking about feeling worried and uneasy. For example: "Her parents were anxious and concerned when they heard the news of the accident."
They must have known that I and thousands of other native Jerusalemites were watching in shock, anxious and concerned about the future.
Results: Significant differences (Wilcoxon test) were found for warm (P=.007), anxious and concerned (P=.004), interested (P=.008), sympathetic (P=.046), and satisfied (P=.041).
Main Outcome Measures: 10 personality variables were rated on a 7-point scale, ranging from "not at all" to "extremely": these were warm, anxious and concerned, interested, hostile, sympathetic, professional, competent, dominant, satisfied, and genuine.
She was extremely anxious and concerned about her younger brothers and sisters.
The Rev David Paskins of the Wimborne St Giles parish church said, "Everyone is anxious and concerned — it's the unknown that is worrying.
In spite of a rebounding and more robust economy, many in the lower middle and working classes remain anxious and concerned about their futures.
Participants were asked to rate how anxious, concerned and worried they would be on a likert scale ranging from 'not anxious' to 'extremely anxious'.
With Obama under fire for his poor foreign-policy choices and indecision, Putin presents himself as a wise and balanced leader anxious to protect human lives, mindful of historical precedents, and concerned about international legal norms: From the outset, Russia has advocated peaceful dialogue enabling Syrians to develop a compromise plan for their own future.
Looking very serious and concerned.
Tense and concerned, but quiet.
People are angry and concerned.
