What to add if low-carb muffins don't rise and are crumbly
Your recipe has no gluten in it. Baked goods without gluten tend to have a crumbly texture; muffin batter usually contains at least some wheat flour, which contributes gluten toward the muffin's structure. The Kitchn has a good blog post about using vital wheat gluten, which can be added to a recipe that is in need of a more bread-like structure (assuming no dietary restriction on gluten). If you add too much, you'll have to adjust the other ingredients in the recipe to compensate (mainly liquids, but possibly fats as well) but a little goes a long way; for your recipe, one tablespoon might be a good starting point.

Vital wheat gluten does contain similar carbohydrates to those found in regular wheat flour, but much less; where regular flour is almost entirely carbohydrates, vital wheat gluten is mostly protein. Consult the nutrition info before you buy it if you're worried about adding carbs to your recipe.

Adding gluten can also affect how the muffin rises, so you might find that's enough on its own; but it's not directly a leavening agent. More good info here: What does gluten &quot;do&quot; in baking?