I don't know that any of us that respond in here are medically qualified dieticians. I'd recommend you consult one or two if you haven't already. Don't chose one that is advertising for a diet weight loss programs though.
As for your gut's bacteria and other stuff being destroyed by antibiotics, there are some recovery treatments for those that had extreme circumstances of that. But they are, I think, something that needs to be handled by a medical professional.
You say you can't tell how many Calories you need. Your scale is the final determination. If you are at the weight you want to be, then are probably getting the overall Calories you need.
If you can't tolerate carbohydrates, then you'll have to rely on fats for your energy consumption. Your body's conversion of fat to energy is a fairly steady process. It doesn't increase very much with activity level. So eating fats while riding probably won't help any. I'm certain that if you aren't way below a healthy weight that your body has plenty of fat.
Even if you could tolerate carbs, you can't replace all the energy spent during your ride. No matter how good a shape your stomach and gut are, they can't absorb Calories at a rate fast enough to replete all that you are using.
So you are what you are. Stay at or below a pace that lets you finish whatever length of ride you are going for. If you wish to get faster, that will come with time, or you can add some intervals where you go all out for a short period till you feel almost drained. Then drop back to a pace you can handle and let yourself recover, then do it again. And again, and again.
Even with that, it takes years of riding. Especially if you are up in years.