I have a rash around my anus.

Literal

Anus [possessive-の] around [locative-に] eczema [subject-が] exists.

A frank medical complaint. 肛門 (こうもん) 'anus' is the formal/medical term. 湿疹 (しっしん) 'eczema, skin rash'. まわり ('surroundings, vicinity'). The construction ~があります ('there is X') is the standard existential for symptoms. Doctor-visit vocabulary.