I have also been diagnosed with all three of these allergies. Fear not, it is possible! I went through my whole life not knowing about these allergies, but found out about 4 years ago, I'm 27. Concentrate on the corn free list first, most all of the foods you'll be looking at, if they have wheat or soy, they very likely have corn derivatives in it as well. I've found my diet is very rich in flavor now, so look forward to that! I get my carbs/starches from sweet potatoes and peas/beans. That should help with some of the bread cravings you'll get as you rid your body of the things it's been used to for a long time (takes about 3 months). If you're starting this diet for the first time, beware that you may feel ill for those first three months, then get really sick for about a week, but then you'll feel the best you've ever felt thereafter! There are a ton of recipes for people with our allergies and they are all awesome, but some take some perfecting (just run a Google search for what you want to make and list the allergies, the brownies are to die for)! Count your eating out days goodbye, though. Restaurants are very tricky to navigate; many won't cater to these allergies together, none of them will lower the price of your meal even though your allergies take away 60% of the typical serving, but you can get an occasional free meal when they cause a hive reaction!
Oh, and if you like salads, make your own dressing! I use 50/50 100% grapeseed oil and white wine vinegar and add dill weed, onion powder, and whatever other spices you like, makes a great vinaigrette and you can take it to restaurants and feel confident you can avoid your allergies with a sale, although, avoid chicken in restaurants at all costs, every one I've been in that serves chicken marinates it an oil (typically olive), which for restaurants, means they use an oil that is mixed with vegetable oil (corn).
It's hard to do this come turkey, so if you can stand your reactions, I recommend weening yourself off slowly.