Then explain your problem to the shoe salesperson. You want both heel cushioning and arch support. Ask for suggestions. Try on at least 3-4 pair from different makers.
6 weeks ago I bought Saucony 3D Grid cross-trainers. I felt an immediate improvement, at least equal to what I've gotten from ice, Naprelan and stretching. I explained my problem to my boss & co-workers and I get no complaints about wearing them to work. The right shoe for you might be New Balance, Nike, Reebok. I suspect it should be pretty stiff.