must vs. have to
In grammar books, I read that "must" is most often used when the obligation comes from the speaker, while "have (got) to" is used when somebody else is the source of the obligation. However, listening to everyday AmE, I get the impression that native speakers (mostly AmE) don't differentiate between "must" and "have to" and use "have (got) to" most of the time whatever the source of the obligation. "Must" seems to be used mostly in formal contexts. Is that true? Do you see any differences between the following sentences? I don't differentiate between them much, and in normal speech I just use "have to" (I'm told most Americans do that too). I'm especially interested in AmE, but BrE point of view is welcomed too.
I have (got) to clean my bedroom. (somebody else wants me to?)
I must clean my bedroom. (I want to?)
(do you see any difference between the two above?)
Must you be making that noise? (formally "Do you have to be making that noise"?)
Romeo must die. (formally "there's a need for Romeo to be dead?")
Just to be clear, I have in mind the present or future affirmative meaning of "must" and "have to". I'm not talking about meanings like "I must have done it" or "I must not go there" etc.
Please note that I'm not a teacher.