Is it permissible, from a Sharia perspective, for a doctor to insert his finger into the anus for examination, given that there is no pain in this area, and knowing that the complaint was about a urinary tract infection and abdominal pain?

This matter is normal, as the basic principle is that the physician does not touch this area except out of necessity. Scholars have explicitly stated the permissibility for a physician to look at and touch the 'awrah (private parts) out of necessity for examination or treatment, even inside the vagina. Furthermore, while covering private parts and shameful areas is obligatory, it is permissible to uncover them for necessities and needs, such as a physician's examination for the purpose of treatment.