不需要。
详见:
Every student who applies for an F-1 visa for the first time will have the SEVIS number of the first I-20 issued written on that visa. However, students may use the same visa (if it’s still valid) to leave and reenter the U.S.—even if they have a new SEVIS ID number—as long as they have not been out of the U.S. for more than 5 months. That is the only rule regarding the legality of your visa that you need to be concerned about.
You do need to pay a new SEVIS I-901 fee ($200) since you have a new SEVIS ID number.
需要,换学校都是需要重新申请学生签证的。