する in 恋をする means "do". So I sense activeness in this phrase. We use 恋をする for both 片思い(one-way love) and 恋愛(relationship). Anyway since it has 'active' meaning, I make images from the phrase 恋をする, such as writing a letter to tell his/her the love, waiting for a response from him/her over smartphone, wasting time by thinking about him/her and so on.
恋に落ちる exactly means "fall in love". From the word 'fall' I sense 'irresistability'. Sometimes I also feel 'astray' or 'off the track' meaning from it. So I think it's basically not suitable for relationship between adorable students. It smells more dangerous.
私はあなたに恋をしました This is grammatically perfect but sounds too polite. To tell love, excessive politeness sounds awkward in colloquial communication. It sounds like reading a story. But I think it's good in writing.