I need to know if there is a substitute for half-and-half (~10%) cream because I am baking a cake without it and I am allergic to it.
When I am substituting in a recipe, I usually use coconut cream instead of cream or half and half if called for in a recipe. (There is a question posted here that covers how to get the cream from a can of coconut milk.) Sometimes I use soy creamer, but sometimes that can be hard to find. I'm sure you could experiment with a mix of soy creamer and soy milk.
My ideal solution is to use vegan recipes to start with, because they are formulated without milk or eggs. Maybe in your case, just look up dairy free cake recipes, if you don't mind eating eggs. There are a lot of cookbooks and blogs out there with a ton of vegan cake and dessert recipes.
Half and half can be pretty closely approximated with one part whole milk and one part cream.
However, if you're allergic to half and half, I would infer that you're allergic to all dairy. In that case, you may well need a specific dairy-free product like a soy-based cream or half and half or coconut milk.
You can also try coconut cream and milk in equal proportions.