It sounds like a faulty/blocked injector cap might be issue, as you mentioned. The other possibility is that the pressure in the barrel was equal or greater than the little bulb could push. You might have tried pouring a glass with the bulb still screwed in to the injector.
IMO, a little bit of air is not a problem, especially if you still have any yeast living in the barrel. Any living yeast should quickly absorb any oxygen that was introduced. But definitely try to keep the tap-air-uptake to a minimum.
Figure our the injector issue, and try again.
If you filled the entire headspace with air (which you didn't) I would venture a guess that you had 2-3 weeks to finish it up, but that's a total guess.