Why does Jane get sent to the red room right after the incident with John, without getting some sort of medical attention or examination for her bleeding head?

I think Jane gets sent to the red room immediately because no one at Gateshead really cares about her health or well-being.  Her being punished for John attacking her and getting her head cut open, just proves the point of no one actually caring about Jane. Everyone at Gateshead (at this point in the book), would rather have Jane sent away and in solidarity than having to deal with her. They all see Jane as  nuisance without feelings, or rather a nuisance with feelings, but whose feelings should be disregarded because they don't matter.