The correct option is C yet
A conjunction's main function is to join or combine two clauses/sentences as one sentence. The type of conjunction used depends on the relationship between the clauses, and whether both the clauses are independent or not. The clauses in the given sentence are both independent, as "She was tired" and "she stayed up to keep her brother company" are complete in meaning, without depending on the other. Hence the conjunction that joins these two is the word that remains, "yet" which is an adversative conjunction i.e., for sentences which are contrast in meaning, "she was tired" and "stayed up". Hence option B is correct. 'Tired' is an adjective as it modifies the pronoun 'she', by describing her state "tired". It does not combine the clauses, as those formed before and after 'tired' are both incomplete in meaning. Hence option A is incorrect. 'She' is a pronoun in the third person singular form, a person whom the speaker talks about to the listener. It does not join the clauses, as after omitting it the clause "was tired" is incomplete and the pronoun is required. Hence it's not a conjunction and option C is incorrect. 'Up' is an adverb that modifies the verb 'stayed' and it means "to be awake". It does not connect the clauses as when you omit 'up' the clauses formed before and after it are incomplete in meaning, hence option D is incorrect.