Gleevec itself does not directly cause a sore throat in the classic sense. A sore throat is usually associated with virus or infection. But Gleevec can cause swelling in certain areas, including the throat area, and this constriction could cause trouble swallowing, and may even feel somewhat "sore" in that sense. So you would want to define more precisely what you are sensing, and where in the throat the soreness resides. Upper throat (near the entry point) can be associated with certain infections or viruses, and middle throat with others. Is the throat tight (constricted) as well? If so, swallowing pills will be more difficult, which can show that your throat is constricted. Have you had your tonsils removed? They are part of the lymphatic system, and are associated with fighting infection. Try to be precise about your symptoms, and then your doc needs to run as many tests as are available.
Although Gleevec does not directly cause a sore throat, it could be indirectly responsible. At this early stage in your treatment you are caught in between two stages. You are killing off the large numbers of leukemic white blood cells (WBCs) that were somewhat functional in protecting against viruses and infections, but your good (non-leukemic) WBCs are just ramping up production, but may not yet be adequate in numbers. In this "in-between" stage you can be somewhat more vulnerable to virus and infection, and fighting an active issue could be more difficult. And any throat constriction could make it worse.
Your doc should continue to try to find an answer for the sore throat, since they can sometimes be a serious issue. Try to be more specific about the symptoms, if possible. If the soreness happens to be high in the throat, a good remedy is gargling every couple hours to kill off viruses or infections. You need to get the mouthwash as far down the throat as possible.
The early stages are tough. We have all been there and know what you are going through. Things normally get better over time.
As a new member, you might want to read this posting for some encouragement:
http://community.lls.org/thread/2600?tstart=0