Is it permissible for someone else to perform Umrah or Hajj on my behalf due to a phobia that prevents me from leaving the house and renders me unable to perform these rituals myself, and am I considered among the incapacitated mentioned in the Hadith?

The sick person for whom it is permissible to delegate Hajj and Umrah (definition) is one whose recovery is despaired of and who is unable to perform them himself due to old age, an incurable illness, or similar circumstances. This is based on the Hadith (definition) narrated by Ibn Abbas: "A woman from Khath'am said: 'O Messenger of Allah, my father reached the obligation of Hajj as a very old man, unable to sit firm on his mount. Should I perform Hajj on his behalf?' He said: 'Perform Hajj on his behalf.'" As for the questioner's illness, recovery from it is not despaired of, and he should seek treatment and try to overcome the phobia. Therefore, delegation is not permissible for him.