up to my neck vs up to his neck

up to my neck and up to his neck both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to my neck	No	Yes	No	No
up to his neck	No	Yes	No	No

As adjectives, up to my neck and up to his neck are synonyms defined as:

Other synonyms of up to my neck include neck-deep, up to her neck, up to our necks, up to their necks, up to your neck.

up to my neck (adjective)	up to his neck (adjective)
deeply involved	deeply involved