At school, someone smoked in the toilet. I fell under suspicion, although I was not there. Does the head teacher have the right to search me for cigarettes?

I am not familiar with Russian laws, but I will assume that a search of a student's pockets and bags by the head teacher (teacher, school director, etc.) is possible only with the consent of the student himself or his legal representatives (for minors, these are parents or guardians). Exceptions are possible only to prevent an accident or a criminal offense (there is reason to believe that there is a combat grenade, or, say, a knife, with which a student has just threatened to kill a classmate). In any case, you can write a complaint to the higher authority that controls the school.

PS. MARINA MORSKAYA, video cameras in the toilet? Are you serious?

At school, head teachers have the right to everything, this is the highest caste, enlisted by the support of the reigning Satan-Director. None of your ahi-sighs, poking the constitution and convention of the rights of the child in their face will not help them, because if you get annoyed and scream, you have something to hide. The situation is identical with the innocent escaping and hiding from the police. It's easier to just turn out the pockets in silence.
It's another matter if the school is equipped with video cameras, only in this case you have the right to encroach on your innocence, because the camera recorded your innocence in this act. In general, with video cameras in schools it is either easier or more difficult, incomprehensible.