You can definitely find Japanese items without soy at Asian markets (as well as natural markets or supermarkets, though you might have to look harder) - you'll just have to read labels. Most udon and ramen have soy, though I've found one of two that don't. Bummer that you're allergic to rice too! But you could eat sashimi. Avoiding soy is way more challenging than I ever would have thought.

Bottom line is that you'll probably want to cook a lot more of your own meals and ask lots of questions at restaurants. A Chinese restaurant I went to recently was happy to point out soy-free items and leave soy out of another item that usually had it.