H3 2006 cylinder head issue

I am new to this forum, a female with an H3 2006 with the vehicle in the shop as we speak.  I am told a new cylinder head will solve all the problems as my vehicle is one of those with the pre vin listed in the site with possible problems.  My vehicle has a little over 9500 miles, and I am not happy about this.  I called the GM rep about an extended warranty as others have done on this website and I was told I will have no problems once it is fixed and they will not issue one.  I am very saddened by GM and their response.  I was given a case number, called my service manager, who guarantees no more problems.  Should I be worried?  I know nothing about cars but feel by reading these forums I do have something to worry about.  Any advice is appreciated.  And I have to admit my dealership has a revolving door when it comes to workers and managers.  So today being told don't worry does not make me feel better.  Once this cylinder head is replaced is that a done deal and I am ok?
Thanks to anyone out there with more knowledge than I.