Do outer ear infections spread to the middle ear?

Not typically: If the tympanic membrane (eardrum) is intact, it serves as a barrier that protects the middle ear from organisms which may enter the external ear canal. If the tympanic membrane is perforated (e.g. From trauma) or surgically opened (e.g. For ear tubes), then there is a direct route for passage of infectious organisms from the outer ear into the middle ear space.

Unusual: The tympanic membrane (ear drum) seperates the outer and middle ear. An outer ear infection can't spread to the middle unless there is a perforation (hole) in the ear drum.

Very unlikely: In order for an outer ear infection to get to the middle ear the ear drum must break open in some way. Far more likely for a middle ear infection to lead to an ear drum perforation and the pus coming out into the middle ear.