My teachers often tell me, "each other" is used between 2 people, while "one another" is used more than 3. Is it like this?
Hmm...yes, usually. I think that rule is a good one to stick to, since that's pretty standard. However, don't be surprised if you see slight variations, since people sometimes use them interchangeably.
"One another" is the more important one to remember. It's used with a large group of people, or even with all of humanity. It's a lot more broad. For example: "people should trust one another." or "they looked around at one another."
"Each other" is usually used with two people, though occasionally it's used with a small group. It indicates a reciprocal action. For example:"let's give each other our contact information."
Does this rule exist? Apparently so.
Do you have to follow it? No, because it doesn't reflect how native speakers use these phrases.