It's not a children's book. I probably read this book 20 years ago and it was not a new book then. I'm guessing it was written some time between the 40s and 60s, but that's just a guess. The book takes place in a society where there have been lots of treatments for genetic diseases, so people who used to die before child-bearing age weren't, passing the diseases along, and health of the population was therefore less robust. (Plus possibly the cost of treatment.) So people were only allowed to get medical treatments, vaccinations, etc. if they were sterilized. I seem to recall people living in a sort of health-care ghetto and many people being anti-health care.
Stump the Bookseller
New format, same book stumper solving.
This sounds like ‘The Bladerunner’ by Alan E. Nourse (1974). (It shares its name but little else with the 1982 film ‘Blade Runner.)
“The novel’s protagonist is Billy Gimp, a man with a club foot who runs “blades” for Doc (Doctor John Long) as part of an illegal black market for medical services. The setting is a society where free, comprehensive medical treatment is available for anyone so long as they qualify for treatment under the Eugenics Laws. Preconditions for medical care include sterilization, and no legitimate medical care is available for anyone who does not qualify or does not wish to undergo the sterilization procedure (including children over the age of five). These conditions have created illegal medical services in which bladerunners supply black market medical supplies for underground practitioners, who generally go out at night to see patients and perform surgery. As an epidemic breaks out among the underclass, Billy must save his city from the plague”
https://en.wikipedia.org/wiki/The_Bladerunner