To be honest, I don't know how you go about changing supervisor at my uni as I've never looked into it, but don't you feel guilty about it!
My last minute advice would be to stay calm, and stick to the facts. Don't get emotional, just go in there, tell them you are worried as you have submitted work (it would help if you had evidence i.e. print outs of emails with dates and times) and you haven't received any feedback. Just reiterate you are worried about completing within the timescale and see what they say. Make sure it isn't personal and say something like, "I appreciate everyone is busy but..."
I've done a very quick google search and found this: http://www.mindtools.com/pages/article/newLDR_81.htm which talks about conflict resolution and has some useful hints and tips.
Good luck and let us know how you get on!