How is the response to Istikhara, and is the distress that occurs after the prayer considered a response?

The feeling of distress after performing Istikhara is not the response to it. While a feeling of relief is a sign one may take comfort in, its absence or the feeling of distress does not mean that there is no good in the matter. The true sign of Istikhara's acceptance is to turn away from the matter such that the heart is no longer attached to it, as stated in the Hadith: "Then turn it away from me and turn me away from it, and ordain for me good wherever it may be, then make me content with it." Therefore, as long as this turning away has not occurred, proceed with what you have resolved to do. There is no harm in repeating the Istikhara. As for the possibility that the cause is a demonic touch or magic, trust in Allah and reliance upon Him are among the most important means of protection. And whoever relies on Allah, Satan has no authority over him, as Allah Almighty says: "Indeed, he has no authority over those who believe and rely upon their Lord." So, if you are sincere in your reliance, the possibility that the distress is from Satan or magic is very weak. However, if there are sins or transgressions, then the possibility is present.