Sister and Brother are capitalized in the same way as Doctor -- when used as honorifics or titles. These particular titles, along with "Mother" and "Father", are commonly used by religious orders. You wouldn't capitalize them (or "mom" or "dad") when used with an article or possessive pronoun.

Is brother capitalized?

Siblings: Brother, sister

In general, don't capitalize words like brother and sister when using them to address someone. These words (and the derivative bro and sis) are more often used as generalized forms of direct address in casual speech than as kinship terms for siblings.

Should family member names be capitalized?

When terms denoting family relationships are used as proper nouns (as names), they are capitalized. However, when the terms are used as common nouns (not as names), they're not capitalized. ... It's easy to get confused about whether you should capitalize family names in your writing.