Meaning of the verb shrink

I used to know the meaning of the verb ‘shrink’ as ‘to become smaller’ but I never know that there is also a noun ‘shrink’ as in the following sentence:

So you’re a shrink, huh? She would sure be glad I’m talking to you.

What does the underlined word mean?

Shrink is an informal word for psychologist or psychiatrist.[YSaerTTEW443543]

TOEFL listening lectures: A lecture from an arts class (2)[YSaerTTEW443543]

I used to wonder where the term ‘shrink’ came from. This is what I’ve just found:

Synonyms for ‘psychiatrist’ (definition: mental doctor):

analyst, clinician, couch doctor, deficiency expert, doctor, guru, headpeeper, headshrinker, nut doctor, psychoanalyst, psychologist, psychotherapist, shrink, squirrel, therapist

Synonyms for ‘analyst’ (definition: examiner):

bean counter, examiner, guru, head shrinker, inquisitor, investigator, number cruncher, psychiatrist, psychoanalyst, psychotherapist, questioner, shrink.

Now, ‘bean counter’ is intriguing. But all I’ve been able to find is the following explanation from The Word Detective:

In the retail field, “shrink” also means something like a reduction in profit margin from errors or failure to keep costs down.

An interesting use of this word as a verb is to describe reluctance or hesitation/shyness to do something. I particularly like the expression: I shrink to think, meaning I cannot imagine. There is also the expression shrinking violet describing someone very shy and bashful.