Everything is good, except your underlined sentence should be in passive voice: Several labels have been switched . ) If you say "Bill and Jack switched teams," you mean that they did it themselves - accidently or on purpose. Of course it's ambiguous as to whether Bill went to Jack's team and Jack went to Bill's, OR each of them went to an unspecified (different) team.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
AvangiAnother common usage is "The labels are switched." (the verb "to be" plus adjective complement - past participle as adjective.)