I am not aware of any part of the Constitution which explicitly names "public health" as an exception to anything. Which articles are you discussing?
Furthermore, "public health" is a huge category. Protecting it does not necessarily mean that it allows for the government to force people to get something injected into their bodies. In fact, the left has for years told us, "my body, my choice". They've even managed to get the Supreme Court to give people that privacy.