That is not an auxiliary verb. The verb "am" is the main verb.
The verb "to be" can be an auxiliary verb. But it can also be a main verb.
Auxillary verbs work with another verb. Eg "I am playing tennis." "I have eaten chips." The words "am" and "have are auxiliary to the words "playing" or "eaten", forming the present continuous and perfect tenses respectively
There is no other verb in "I am shy", the verb "am" is the main verb.
In these sentences it is linking the subject (I) with a subject-complement (the adjective "shy", or the noun "a student") when a verb is used to link like this it is a "copula".
So the structure is pronoun-copula-complement, and you could call these "copula sentences".