Continuing on theme of "you haven't given us anywhere near enough information"...
"Nearly getting hospitalized once a month" and doctors saying "you are working out too much" are pretty big red flags. Doctors in front of you are far more credible than strangers on the internet -- listen to them more than you listen to us, even if they tell you things you don't want to hear.
We'd need to know what your symptoms are to be able to take a stab at helping. However, from the information you do give us...
* You get up at 5, and list yourself as in the gym from 5-7.
* You've recently lost a lot of weight.
Let me take a guess at your symptoms: you start getting light headed; your vision darkens at the periphery; sound seem to echo strangely; you break out into a cold, prickly sweat; you feel like you're going to vomit; stopping and standing still doesn't make things better, but you have to sit or (better yet) lie down.
I've had this happen before -- it's what happens when your blood sugar crashes because you haven't eaten recently enough before working out. Like, say, if you work out on an empty stomach immediately after waking up, or if you work out at the end of a work day in which you skipped lunch because you were too busy. Or, as is possible in your case, if you're in general not eating enough because you're gung ho about losing weight and make the mistake a lot of people do of assuming "If eating 500 fewer calories than I burn is good, eating 1,000 fewer calories I burn is even better!" Eat something substantial 1-3 hours before working out, and those particular symptoms will stop happening.
And, really, 3.5 hours of sleep per night is not sustainable over the long haul if you're also working out for 2 hours a day. I used to get by on 4-4.5 hours a night in high school, but I wasn't working out nearly that much. The harder you work your body, the more important it is to sleep, as your body repairs the damage exercise does while you're sleeping -- you won't get stronger if you don't give your muscles that chance to heal.