When Sirius first asks after Harry, Dumbledore assures him that Harry is safe and cared for, and that they can talk about it more once Sirius has gotten himself sorted out. Reassured, Sirius does not ask anything further, and allows himself to be admitted to St. Mungo’s. Harry should not see him like this, Sirius reasons, and besides, that’s a lot to explain to a small child, who should be growing up happy and healthy and loved, without knowing about the horrors of the world like dementors and miscarriages of justice. So Sirius focuses on getting better, and waits for Remus to visit him.