Seems cleaning my rim decreases the squeeling but does not stop it altogether.

As far as the other suggestions they are all good ideas. I think I need to do the toe in adjustment. Since I have cantilever style brakes where the pad has a threadless stud sticking out that can only be adjusted in and out for more or less travel. I do not believe I have an adjustment for brake shoe angle but will check closer. My bike is an older Giant Nutra cross bike. Any suggestions?