Calm down. If you've looked around you would have seen that some people apply late Spring and do fine. I don't have personal experience but scholl recommends that to be a priority candidate you should apply before April 1st, at least that's how I interpret it. Also, would you not apply even if you had a small chance of acceptance? The only reason I could see why you shouldn't apply is if you don't meet the school's minimum requirments. Do the research. The real question, or issue, is would you let/want someone like you ( no offense here ) into a program?
Edit: actually I just checked and I can't remember where I saw the April 1st date on Scholl's website. It does say they will accept applications up to July 31st, but they won't take an MCAT past may for matriculation of the same year. I just didn't want to be accused of spreading false info.