I don't think that was what that meant. I think the "throw up" part was in reference to the administering of the enema itself.

I don't believe that is what "throw up a clyster" means. If you google it, that particular phrasing is not uncommon to this story. To me, from context (I have no special knowledge), "throw up a clyster" means to mix a clyster, not regurgitate it.