I understand from friends of mine that medical school is killer and that there really is very little time, so I kind of (from observation only) get what you're saying.
But the thing is, especially when you're in that kind of situation, you have to commit to making time and making it work. It kinda sucks ... I know. And I'm not passing judgment at all .. just saying that as long as you say "it won't work" ... then it won't.
As far as food, it sounds to me like your nutrition sucks.
As a med student, probably the best thing you can do for your future patients is get educated on real nutrition. I don't know what kind of medicine you plan to practice, but in my experience and that of many people I know, doctors know the least about proper nutrition and diet of almost any other group of people. It's kinda sad really.
So let's address that, first.
What you describe as your meal plan sounds like very little ... but if you're gaining weight, then you're eating more than just a bowl of cereal, a sandwich, and some chicken. There have to be other "hidden" things that you're eating - snacks, candy bars, chips with lunch are the usual culprits; snacky things that people don't think about adding to their daily food count. Either that or you're eating a LOT of cereal in the morning and a big, calorie laden sandwich from Subway, and you're preparing your dinner in a really fattening manner. Either way, you're eating more calories than you're burning.
Ideally at your weight, I'd say you should probably consume around 1600 calories a day in order to lose weight (even w/out exercise, although it'll be somewhat slower w/out a good exercise plan). You have to make sure that your meals are nutritionally balanced - as I said above.
Breakfast: If it's going to be 4 or 5 hours until you get to eat again, then sugary coated cereal is a crappy breakfast (just keepin' it real, here). This is the meal that breaks your sleeping fast and has to nourish you for multiple hours until you can eat again. A proper breakfast for you should contain about 1/3 of your daily calories and should have lots of protein and complex carbs. You should be getting 20+ g of protein with your breakfast at least. Eggs, greek yogurt, oats, peanut butter, whole grain toast... stuff like that. Out of your 1600 calories a day, you could easily allocate 500-600 calories for your breakfast. A serving of natural peanut butter folded over in a slice of whole grain bread, a banana, and a glass of 1% milk (you could even throw in a scoop of whey protein for an added protein boost) is a healthy breakfast for you. Or two boiled eggs and some cream cheese on a slice of whole grain toast and the glass of milk. Prep steel cut oats in the microwave the night before and then pop them in to reheat while you're getting dressed in the morning. Top them with yogurt and fruit. Those kinds of things are fast, easy, and portable, if you need to eat breakfast on the run. And those meals contain enough protein and carbs to keep you going through the morning.
Lunch - Subway isn't hideous, but you need to make sure you're making the right choices. Turkey, lean ham, roast beef ... with LOTS of veg, on whole grain, and no mayo. Mustard, oil and vinegar, are all better choices. No chips. No sugary sodas. (I drink diet sodas, but some people feel that no soda at all is better - it's personal choice as far as I'm concerned.)
Dinner - Chicken is fine, but make sure you're cooking it in a healthy way. Make sure you get more veggies with your chicken - even if you just slice up a tomato and sprinkle it with some salt and vinegar or olive oil.
Between those, even though you have limited time, throw an apple in your bag. Or a snack baggie of carrots. Or some edamame. Anything healthy that you can munch on while you're walking or driving. My standby morning snack is an apple with some sharp cheddar cheese - extremely portable and a good filling snack.
And honestly I know you don't have a lot of time, but even if you could knock out a set of squats, lunges, pushups, stepups, dips ... just little things, periodically throughout the day, that will really help with fitness (which helps not only weight loss, but energy levels). I add these things into my daily routine because I sit at a computer all day. So about once every couple of hours, I get up and stretch. I may knock out 2 sets of pushups off my desk. Or when I go to the bathroom, I'll do 15 quick squats. Or to stretch, I'll do a standing squat against a wall and hold it for as long as I can - trying to get to the point where I can do it for a full minute. This is how I fit exercise into my day ... 30 seconds here and 30 seconds there ... and believe me, it makes a difference. The first day I did a 3 sets of 10 step-ups on a straight backed chair during a potty break, I was sore. These sound like small things, but they work.
Like I said at the beginning - make the time for what's important. And being healthy (especially when you're dealing with the stress of med school) is really important.
