It sounds like you need to scale back if your exercise is causing you to become physically ill. I know your inner self is yearning for some hardcore exercise, but you need to let your outer self catch up.
For me, I started just going to the gym for cardio. I did that for a few weeks, 30 minutes every day, until it created a routine, and I felt like the cardio was easier. (Not easy but not impossible-feeling.) Then and only then did I add in weight training. Now I exercise 75 minutes - 90 minutes every day, and I feel great! In fact, I now feel guilty if I don't go to the gym!
You don't want to hurt yourself by pushing too far too fast and then be stuck without any exercise while you heal. Give it time. Your body will catch up with your mind. In more ways than one too. I know what you mean about looking in the mirror and thinking your body doesn't match the work you're doing. But in time - and it won't take long - it will. It took me about a month to see noticeable results from working out regularly. In the grand scheme of things, a month is no time at all!