There are several synonyms for the phrase "stick your nose in," which means to interfere in someone else's business or affairs. One alternative is "meddle," which implies an intrusive and unwanted involvement in a situation. Another option is "interject," which suggests a sudden and unwarranted interruption. "Pry" is a verb synonym that implies a forceful or uncomfortable probing into another person's affairs. "Nose around" is another synonym and means to search or investigate without any specific purpose or permission. Overall, these synonyms capture the feeling of overstepping boundaries and interfering where one is not invited or needed.