up to my neck vs up to our necks

up to my neck and up to our necks both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to my neck	No	Yes	No	No
up to our necks	No	Yes	No	No

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

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

up to my neck (adjective)	up to our necks (adjective)
deeply involved	deeply involved