Hi Tammy,
 
By "size and shape of a half of a split pea" I assume you mean round in
outline, flat on one side, and convex on the other side?  That sounds to me
like the operculum from a small species of Turbo or Astraea (both in family
Turbinidae).  If they are perfectly round in outline they are probably from
Turbo, if oval shape probably from Astraea.  An operculum that size would come
from a shell about 1 inch in diameter.  If they came from the Caribbean area
(you said "up from the south") they may be from the common "chestnut turban",
Turbo castanea.
As for their use in removing a foreign object from your eye, I never heard of
that, but I suspect an operculum in your eye might well stimulate a copious
flow of tears, which might wash out any small foreign object that was there.
:-)
Regards,
Paul M.