All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
When you turn to Allaah in supplication and seek His help imploring Him to bless you with what is good for you and to safeguard you from harms, it is likely that He inspires you with a way out of your problem as you implore Him and turn to Him for guidance and aid. This calls for striving in expressing gratitude to Him and praising Him as befits Him. This is not a strange thing in the slightest; Allaah, The Exalted, answers the supplication of those in need who call upon Him and relieves the distress and harms. Allaah, The Exalted, says (what means): {Is He (not best) Who responds to the desperate one when he calls upon Him and removes evil?} [Quran 27:62] He also says (what means): {And when My servants ask you (O Muhammad) concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me.} [Quran 2:186]
What you mentioned is a manifestation of the kindness and mercy of Allaah and there is no difficulty in explaining that to others. Verily, the kindness and mercy of Allaah have no limits.
As for the Istikhaarah prayer, we believe that when the person performs the Istikhaarah prayer, he should go ahead and do what he is doing Istikhaarah about, and if he finds that the matter is facilitated, then this is a sign that this is good for him; otherwise, he should give it up and know that it is not good for him and be content with the choice of Allaah for him, knowing that it is definitely better for him than his own choice for himself. For more benefit, please refer to fataawa 82964 and 83982.
Allaah knows best.