Rock's comment strikes me pretty believable, especially in a rural community like Andrews, SC. White dentists often refused to treat black patients. Black dentists, like black doctors (see below), were usually scare. Veterinarians could exist as a viable option when no others existed.

Overall, lack of access to medical care was one of the most dangerous aspects of segregation. While some southern hospitals had segregated emergency rooms in attics or basements, many hospitals refused to admit African Americans patients at all. Even African Americans requiring emergency treatment were turned away - for example, a pregnant woman giving birth on the sidewalk outside a hospital that refused her in Birmingham or parents pleading with doctors to treat a son injured in motor accident. Black patients would need to be transported to other facilities, and too often died in the process. Finding white doctors and nurses who would treat African Americans in private practice could be equally challenging.

African American communities and religious/philanthropic groups helped establish their own hospitals over the course of the early 20th century, but these facilities were usually located in larger southern cities and faced serious shortcomings in terms of resources, medical equipment, and space. These hospitals were often staffed by African American doctors and medical professionals, but they too were in short numbers because they could usually only receive training from black colleges (which were hampered by segregation too) or institutions outside the region. For rural towns like Andrews a single black doctor might serve the entire community, like this Ocala, FL, doctor who treated patients on his dining room table. Should a rural community lose that doctor to retirement or migration, and the closest medical facility was hours away, then suddenly a veterinarian might be the only realistic option left.

Needless to say, lack of medical access aggravated serious public health issues within the African American community, but they threatened the whole South. Bacteria and viruses don't recognize race. Black health problems could easily become white problems too. Also, the giant racial disparities in health care obviously violated the "Separate but Equal" legal mandate from Plessy v. Ferguson. Over the course of WWII and leading into the Civil Rights Movement, significant state and federal investment went into providing better medical care. The story of this process is told in a solid book by Karen Kruse Thomas, Deluxe Jim Crow: Civil Rights and American Health Policy, 1935-1954.

A follow on question (and maybe easier to answer): was health care segregated during Jim Crow? Could a black go to any medical doctor or just certain ones? Also what about emergencies, would any hospitals accept injured blacks?

Another follow up question: how were blood transfusions handled? Would they racially segregate the blood supply? Did they even take donations from black people?

I have been studying Jim Crow as part of my degree and yes this kind of thing seems to come up all the time. There were laws in Alabama prohibiting even the meeting of black and white people in the 1930's. I read the autobiography of James Allen, who ran the communist Southern worker which tried to unite black and white workers. (Both the autobiography and all of the issues of the SW are available online) Obviously communist writings often need reading with a pinch of salt but must of what is written there is fairly accurate and backed up by historians etc. It is absolutely mind boggling the extent to which segregation permeated the society, particularly in the South. Obviously there were better and worse places, but it was pretty terrible until really shockingly recently. There are even accounts during WW2 of white American nurses refusing to treat wounded black soldiers, who just had to lie outside the hospital on the ground until some french troops turned up and took them to the french hospital.