Ikes! I feel for you.

Let's start with what CAN you have and build from there. What foods are safe? Do I understand rice is safe? Can you have any legumes, or are all beans off limits? Protein may be a challenge from what I can see from your post.

Deep breaths, deep breaths.

Things you can have??
milk like: coconut milk/cream/oil/flour? rice milk? Depending on where you live there may be some amazing places to get soy-free substitutes. If you're in the US look to Trader Joes or Fred Myers. They may have coconut yogurt. I know it's a thing, but it can be very hard to find depending on your location. Theglutenfreegoddess uses a lot of coconut flour (and almond flour) but her website is amazing and she does have a few vegan recipes. They also do make corn free/soy free gluten free flours. If you can't find them locally, amazon is a magical place.

Egg like: I don't know how new you are to Vegan and gluten-free, but egg free and gluten free sucks. I've been there. Can you eat flax seed or apple sauce? You can often add them in baked instead of eggs. There is also a glutenfree no egg powder I use a bit, but I think it has corn in it- so look carefully. Is it all egg or can you have egg white? Because a lot can be done with egg whites. Gelatine? I don't know how Vegan you have to go, but I've used plain gelatin in the past instead of eggs to pretty good results in a lot of recipes.

Spices: Salt, Basil (seriously so much can be done with it), oregano, cumin, coriander, mint, cayenne pepper, thyme, sage, bay leaves, paprika, mustard, wasabi.

Grains/proteins: Wild rice, buckwheat, chick peas, black beans, broad beans, kidneybeans, lentils?

Chocolate substitute: carob? It's not the same, but almost can be helpful for moods.

Breakfast: hot-rice porrage w/ fruit, fry up with kale, zucchini, and beans. Cold- "yogurt" (coconut) and fruit; fruit with coconut flakes, smoothies

Lunch/dinner: vegetable soups (make your own broth as all broths have onion/garlic; basically add veggies into a crockpot and use the liquid. Or you can use water/ pureed cauliflower or potato). Sushi (double check the seaweed is soy free because I'm not sure). Roasted/stuffed eggplant. felafels (again make your own because store bought likely will have sesame seeds, onion, and garlic).

Dessert: coconut cream milk shakes- place a can on the top shelf of your refrigerator for 24 hours. Mix with your favorite veggies (spinach, kale are my go to), and fruit (apple, mango, pinapple). Also could add carob to this and blend.

Duckykissy is right I am wheat, dairy, and egg free it does suck. Most gluten free Has dairy or egg you really need to watch your labels and know what is in your food. And gluten is in everything that comes in a box bottle or can. If it's not a natural food it probably has gluten.
Good luck with the new lifestyle.

It does seem overwhelming but once you find recipes that work for you, you can start to tweak them to your liking and nutritional needs and you'll be just fine.
I am in a diet limited of carbs and at first I thought I was gonna die without bread. But I have found that if I add lots of veggies to my diet, I don't really miss the grains.
I second the question about meat. Are you allergic to meat? Why can't you have meat?
If you must substitute meat, you can make dishes in which veggies are the main ingredient. Cauliflower, broccoli, eggplant, beans, squash, pumpkin, potatoes. The fact that you can eat rice is a huge plus. Rice goes with just about anything. Try Asian food recipes, South American, and tweak them when they ask for an ingredient that you can't have for something you can have and can be a good substitute.
For example I can't have flour, so I found a soup recipe that is supposed to have flour as a thickener. I found out that some thicken their soups with bulgur for lower carb meals. I haven't tried it yet but I sure will because flour is off limits.