Is my behavior of raising my voice at my sick mother, who has become like a child and does not let us sleep, Islamically permissible, especially given that she is not bothered by it? And what should I do?

Allah commanded that parents be addressed with politeness, gentleness, and humility, and He forbade scolding them or speaking harshly to them. He said, exalted be He: "So do not say to them, 'uff,' and do not repel them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they nurtured me when I was small.'" (17:23-24). The "noble word" is the word of the sinful servant to the harsh and stern master. It is not permissible to raise one's voice with the intention of scolding the mother, even if she does not get angry. As for raising one's voice with the intention of making her hear, there is no harm in that. You can consult a doctor to find a suitable way to deal with her. Your patience with this and your dutifulness to your parents are among the best deeds and acts of obedience.