This is quite subtle and it is when 'must' equals an imperative need to do something, rather than an obligation as the following examples will illustrate:
Je dois aller chez ma mère ce matin, elle ne va pas bien.
Je dois aller aux toilettes.
Je dois passer à la banque, je n'ai plus d'argent.
You would use 'devoir' rather than 'avoir besoin de' and as you have noticed it is followed by another verb in the infinitive.
Hope this helps!
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