Specialty beers (which are becoming increasingly common) can be very confusing, but once you've read all the introductions to the categories, sections, several time you can see through some of the code.
In the BJCP, it would be category 30A. Spice, Herb or Vegetable Beer. (in Australian Amateur Brewing Championship Styles it's category 17.2)
The category description (unfortunately missing from the AABC guidelines) has a lot of helpful information here (i've bolded the relevant bit):
30. Spiced Beer
We use the common or culinary definitions of spices, herbs, and vegetables, not botanical or scientific ones. In general, spices are the dried seeds, seed pods, fruit, roots, bark, etc. of plants used for flavoring food. Herbs are leafy plants or parts of plants (leaves, flowers, petals, stalks) used for flavoring foods. Vegetables are savory or less sweet edible plant products, used primarily for cooking or sometimes eating raw. Vegetables can include some botanical fruit.
This category explicitly includes all culinary spices, herbs, and vegetables, as well as nuts (anything with ‘nut’ in the name, including coconut), chile peppers, coffee, chocolate, spruce tips, rose hips, hibiscus, fruit peels/zest (but not juice), rhubarb, and the like. It does not include culinary fruit or grains. Flavorful fermentable sugars and syrups (agave nectar, maple syrup, molasses, sorghum, treacle, honey, etc.) can be included only in combination with other allowable ingredients, and should not have a dominant character. Any combination of allowable ingredients may also be entered. See Category 29 for a definition and examples of fruit.
In the case of Category 30A. The entry instructions say
"The entrant must specify a base style, but the declared style does not have to be a Classic Style." So in essence, you've got a base beer style (Sweet Stout aka Milk Stout), and you've added to "spices" (in this case nuts) to it. If you were playing around with Maple Syrup or another fermentable sugar, or a fruit, you'd probably then have to go into the Experimental (BJCP) category or Specialty (AABC).
Depending on how it tastes (don't oversell an ingredient if it's in the background), you might describe it as a Sweet Stout with hazelnut and carob. If it is really strong in one of the flavours (eg hazelnut) you might want to say "Hazelnut Sweet Stout with Carob". This is just about setting the judges' expectations so they know what they should be looking for (it might not make a difference, but it certainly doesn't hurt).
Likewise, if you think judges won't know what carob is supposed to taste like, you could include that in the comments (I only remember it tasting like crappy cacao/chocolate, so might need some reminding.