Hola Garry

You can include the pronoun and make it more "personal" so it is "you" who is experiencing that "Me daban escalofríos" ( in this case we´d prefer to use the verb in plural)

In the text, it's omitting the use of pronouns to give that effect of "an impersonal sentence" as if it is referring to a general feeling that "anybody" would experience if they were in that situation. That also triggers a verb in the singular making it more of an impersonal sentence: "Daba escalofríos"

Saludos