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				I also have never heard of a collapsed trachea in a puppy that's only 6.5 months old.
			
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  Let me introduce you to my dog.  Got him at 5 months old and he already had it.  Sadly, it's terribly common in Yorkies to have this, sometimes from birth.  The average age of onset is 7 years, however there is a second spike in onset for young puppies.   
CT is different in Yorkies than in many other larger breeds.  It's caused by a genetic defect that makes the trachea really weak.   
It can occur deep down in the thoratic region of the trachea (deep in the chest).  An early onset would sound a lot like what you are describing.  I'm not saying that it IS CT, but it certainly could be.  If the coughing sounds like a kinda honking noise, then it's downright probable. 
The x-ray should let you know...Good luck, my thoughts are with you two. 
Edit:  Oh, you might want to try a tracheal massage to see if this causes a coughing fit...if so, then that's another indicator.  Massage the throat for 1 minute along the trachea and see.   
Also, puppy-onset CT can be linked to other respitory problems.  If the troublesome spot in the lungs was some pnemonia, then that could lead to CT developing early in a pup with the genetic predisposition.