Dr. Terrell served as a medical doctor for many years in Lea County. In 1941, he purchased the Shuler Hospital from Dr. A.C. Shuler after Dr. Shuler announced that he was relocating to Carlsbad to join the Womack Clinic.

The building where the medical practice and hospital was located was going to be renamed the Terrell Hospital. It had been built in 1931 and was once of the first brick buildings to be built in Hobbs. It could accommodate six patients.

An article in the Hobbs Daily News-Sun on February 16, 1941 recounted that Dr. and Mrs. Terrell had lived in Hobbs for the past eleven years and that the former owner, Dr. Shuler had lived in Hobbs for five years. The article continued that no changes were anticipated in the operation of the hospital following the change of ownership.

Dr. Price was the son of Albert Pinkney Terrell (1852 – 1914) and Bennora Trabue Terrell (1861 – 1942). He was born to the couple in Kentucky on December 16, 1884. Allen P. Terrell was living with his parents and four siblings in Missouri in the 1900 census. By 1910, he was about twenty-five years old, single and was working as a physician in Dallas, Texas. He was living with his parents and two siblings. Dr. Terrell served in the field artillery during World War I at the rank of major. By 1920, Dr. Terrell appears to have been living in Wichita Falls, Texas, was single at the time and was practicing as a physician. He relocated to Hobbs, Lea County, New Mexico in 1929.

Dr. Terrell was last married to Maude Hawkins Terrell (1888 – 1967). Mrs. Terrell was a nurse by profession and during the time in which they owned the Terrell Hospital in Hobbs worked and helped to manage the facility.

Dr. Terrell passed away in 1947 while still living in Hobbs, New Mexico. Mrs. Terrell survived him by another twenty years and both are buried in Riverside Cemetery near downtown Wichita Falls, Texas.