Its not uncommon for a tank that has been moved to go through a "mini-cyle" As NaCl_H2O said, it sounds like your are well into it now. Water changes skimming, and carbon will help out a lot. I would also anticipate that you may have an algae bloom somewhere in the near future. Its to be expected, just be prepared for it and ready to respond. Adding some phosphate binder might help head it off.

I moved my tank across country 3 times in a 14 month period. I've been there and know the drill. Good luck and welcome to MAAST.