First of all, it is important to note that searching a locker or a cell phone does not really bring up First Amendment issues. Instead, such searches have to do with the Fourth Amendment. The First Amendment comes into play when we decide whether to punish students for certain types of speech. In this case, the issue would be whether cyberbullying is a form of free speech. There are two possible issues, then: does the 4th Amendment allow teachers or other school officials to search lockers and cell phones and does the 1st Amendment allow schools to punish students for cyberbullying?
The answer to both of these questions is in some ways a matter of personal opinion. On the second question, you have to decide for yourself is whether cyberbullying disrupts the educational environment. On the first, you have to decide whether searches of lockers and cell phones are reasonable in the given circumstances.
Public school students have the right to free speech, but schools have the right to maintain an environment that is conducive to education. Schools may therefore ban speech that disrupts education or that goes against what the school is trying to teach. This is why, for instance, schools can ban t-shirts with pro-drug or alcohol messages. The question you have to answer, then, is whether cyberbullying disrupts the educational environment enough to warrant depriving students of their right to free speech (in other words, their right to say mean things to one another over social media).
Public schools also have the right to search students’ possessions in more circumstances than police can. School officials do not need probable cause or a warrant to conduct a search. Instead, they have to have a reasonable suspicion that someone has violated the rules. If they have a reasonable suspicion, the search has to be reasonable in its extent. In other words, it cannot be any more intrusive than it has to be. So what you have to decide is whether searching a cell phone is excessively intrusive if there is good reason to suspect that someone has been bullying someone else online.