Potatoes aren't grains, but I understood they break you out, too? That's a bummer. You could perhaps try soaked and fermented buckwheat and soaked dark rice and try small amounts with meals, and see if you fare any better.
I don't avoid fruit and eat quite a lot of bananas, actually. I don't count any macronutrients anymore, but I'm now eating quite a lot of carbohydrates. Mostly my diet consists of eggs, vegetables, potatoes, rice, buckwheat, butter and olive oil, bananas and other fruit, avocados, some liver and meat. A bit of dairy besides butter, but I'm trying to avoid it. And coffee but I'm trying to quit. I used to be more or less clear, but since starting fairly intensive studying at my new school, I started to get inflamed acne again (back when I was clear, my diet was the same, except I ate a lot more dairy). I still have some inflamed acne, but since I started taking fish oil a few months ago it has gone down quite a bit and seems to be getting better. I actually don't have any active acne at the moment, although it's a first for a while, heh. When I do break out, they're usually mild surface pimples but I do get occasional cysts. I usually clear when I'm not stressing and get lots of sleep.
Oh, and when my boyfriend is over, I actually eat a lot more unhealthily, e.g. gluten-free pasta, home-made gluten-free pizzas, popcorn, chocolate etc, and my skin always tends to worsen and get oilier even though I stress a lot less. So diet must have at least some significance for my skin. I've also noticed that my skin might be oilier when I eat more fat, but I'm not sure about this yet.
It's good you consume at least 40-60g of carbohydrates. It might be enough for you, but I guess this does depend on the person and other lifestyle and health issues. If you seem to be having issues, then try adding carbs and see what happens.