"Teacher, please help me."
I live in China now and people have always told me that 帮助 is used as a noun and 帮 is used as a verb. Is this true? If so, shouldn't this sentence be "老师，请帮我"?
As a Chinese native speaker, both 帮 and 帮助 can be used as a verb, the nuance is that 帮 is more informal and colloquial, while 帮助 is more formal. Either 帮 or 帮助 is seldom used as a noun.
Furthermore, there is another match, though not perfectly, in Chinese and English: 请帮我一个忙。 <-> Please give me a hand. Here 忙 can be grammatically understood as a noun, but that cannot be translated directly, like "hand" in "give me a hand".
I would use 帮, but I don't think 帮助 is wrong. You won't hear a lot of people saying 帮助 in that sentence though.
The English sentence's sense of urgency is lost in the Chinese. It's more like 老师救我
A less awkward way of saying this would be: "老师, 您 能不能帮助(or 帮帮)我." Using the polite 2nd person pronoun (您) here eliminates the need for the word please.