Anxious is the adjective and has two main meanings.
1. a feeling of worry, nervousness or unease
I was very anxious about my test results.
2. eager to do something or for something to happen
I was very anxious to to see the new superhero film.
So the first sense always describes a negative form of nervous energy but the second one describes a positive form of it.
Anxiety is the noun and is almost always used in the first sense of the adjective.
- a feeling of being anxious
I felt a lot of anxiety about the test results.