Normal IgE but still blaming allergies?

I have had a wicked time trying to get my lastest asthma attack under control (2 specialists - 3 different appointments and 4-5 visits to family doctor, all within the last 6 weeks).  

The respiralogist who I just met last week for the first time seems to be determined it is my cats that are the trigger.  However, my blood tests came back negative for everything tested and normal IgE levels.  All my other antibodies, celiac disease screen, complement proteins and C reactive proteins are all normal as well.  I also did skin ***** tests with all negative results, except the histamine control.  

I did test positive for cat allergies 2 years ago which we did allergy shots for and symptoms completely cleared up and I haven't had any symptoms in months with any cat.

How can I have all these problems with my asthma when blood tests show no allergies or inflammation?  I don't understand how the cats could be causing the asthma attacks.  Hopeful someone has some ideas.  Thanks!

[Tammy2009]

I'll give my blood results if that helps.

IgE 3.1kIU/L  (the reference they give is that "95% of adult values fall between 0 and 160kIU/L with geometic mean value of 17 kIU/L")

IgG is 11.04g/L - reference 6.8-18.0