A school official might have the legal right to search you (without a warrant), if, following New Jersey v. T.L.O, they have a reasonable suspicion that the student has done something wrong (not necessarily a crime). However, students do have a reasonable expectation of privacy. The court ruled that schools do not have the same complete right to invade their child's privacy (likewise, schools do not have the same right to suppress speech of children). If the counselor has a reasonable suspicious of wrong-doing, a warrantless search would be legal.
It does not follow, though, that a student may resist such an order without consequences. The courts, and not the student, will determine whether the suspicion is reasonable. There does not appear to be case law establishing one way or the other whether the official must even articulate a reason for the search (students relent and sue later). A student can "legally" refuse the search (the official cannot batter the student to perform the search); but there probably is a rule that if you refuse a search request, you will be suspended (such a suspension was upheld in DesRoches v. Caprio). Picking Portland as a random district in Oregon, they do state that "The school may search a student if the school has a reasonable suspicion that a prohibited or dangerous item will be found". They also articulate disciplinary procedures for student violating the rules, and on p. 12 include a broad form of prohibited misbehavior, "refusing to follow directions". They are supposed to engage in lower-level discipline ("conferences", with school officials, which parents may attend) before imposing stiff penalties such as expulsion.
Suppose a student had been in an accident years before and had disfiguring scars on his forearm. An official could not search the students arms to satisfy voyeuristic curiosity: there is no reasonable suspicious of wrongdoing. Suppose on the other hand the student had needle tracks on his arms from drug injections: a rumor to that effect would create a reasonable suspicion that the student was abusing drugs. You can sue to find out if their suspicion was reasonable.