Are you saying that your stem now looks like the center one in the pic you provided? If so, you broke the shaft that goes through the core. Since your tire is not completely flat, the remaining portion of the shaft is still sealing the valve so you should be able to top off the pressure and continue to use the tube. When it loses enough pressure, the internals will fall into the tube and you will not be able to pump it up any longer. If you are lucky your tubes have replaceable cores. If not you will have to buy new tubes.