RAST testing

I recently had a RAST test done.....the IgE blood draw kind.  The results came back indicating that I had no allergies.....  I've long been unable to identify what "triggers" my asthma.  My question is -- how reliable is the blood testing --- is the actual skin testing more or less reliable?  A couple items that weren't on the screening were oranges (which used to make the corners of my mouth irritated enough to crack) and peeled Italian plum tomatoes (which, when I've handled them to chop them smaller while cooking, cause my hands to itch so that I have to run them under cold water and get the juice off).  Could I be allergic to those two items and should I mention those to the doctor?  Reason for the tests were to determine whether or not I had allergic asthma.