Just plain messy, get a good 3m filter cartridge respirator. Put a fan in the window and blow all the dust out.
Just take it all down to the bare studs, this will be your best way to go about insulating and sheet rocking and any other issues you may not be aware of.
Going over plaster is like putting on a bandage without cleaning out the wound. Start fresh, trust us, this results in less headaches. Many folks can insulate and Sheetrock themselves, these are the easiest of the DIY trades besides painting.
GO to the library for a FREE book on old construction if you are worried.
I have been doing it for 25 years, we can get you through this.