What was a big problem facing American medical care in the first half of the nineteenth century?

Perhaps their biggest problem at that time was a lack of
technology and medical knowledge.  Scientists still didn't understand how disease was
spread and were unaware of the existence of germs, so even trained doctors had little
means of disease prevention, and little more than that to treat
them.

Doctor Benjamin Rush, considered one of the nation's
leading physicians and researchers in the early 1800s, prescribed Lewis and Clark's
expedition healthy doses of "Rush's Thunderbolts", a laxative so powerful that sick men
taking it would probably have been better off taking nothing at
all.

Another large problem was access to trained doctors. 
In the small towns and rural areas where most Americans lived, the best you could
usually hope for was a "country doctor", who was usually little more than a glorified
nurse.  First aid responders today have much more sophisticated knowledge and skill than
most doctors of the time.