Is it permissible to combine and delay the Maghrib and Isha prayers due to the doctor's clinic being far away and the fear of the Maghrib time expiring before reaching it, knowing that the journey began before the Maghrib adhan and the possibility of searching for a mosque existed, but the fear of missing the doctor's appointment prevented it? And if it is not permissible, what is the expiation?

It is permissible to combine two prayers while at home for an absolute necessity, provided it does not become a habit. This is the view of a group of scholars, including Ibn Sirin, Ashhab, Al-Qaffal, Al-Shashi Al-Kabeer, Abu Ishaq Al-Marwazi, and a group of Hadith (definition) scholars. Ibn Al-Mundhir and Ibn Taymiyyah also chose this view. They cited the hadith of Ibn Abbas: "[The Prophet] desired not to burden his Ummah." Therefore, there is no blame in what you did, as you were in need. However, according to the majority opinion, you must search for a mosque to pray Maghrib, then continue your journey. It is safer not to repeat this again and to strive to align with the majority opinion regarding not combining prayers except for a permissible excuse such as illness, travel, or rain.