I'm not completely clear about your question, but I will answer with the 2 possibilities. If you are asking about actual medical care the answer is very primitively. There were no antibiotics, no vaccinations, little anesthesia and no widespread acceptance of the germ theory of disease. Communicable diseases such as smallpox, measles, dysentery, and many others were major killers.
If your question is what medical benefits did the government or the military provide to wounded soldiers after the end of the war, the answer is limited care. Confederate soldiers received little or no benefits. Union soldiers and their families received payments. Before the Civil War there were a few homes for wounded soldiers and after the Civil War more were set up. The following website: http://www.va.gov/health/NewsFeatures/20110413a.asp provides a brief history of soldier's homes post Civil War. These homes eventually led to the Veteran's Administration and other veteran's benefits.