Hi - it sounds like you are really stressed, and time-short, to boot.
First, losing weight by skipping meals is NEVER a good idea. You set your body up for having problems, later, and apart from that, it can cause your blood sugars to take a nose-dive when you go too long without food. This in itself can cause fatigue, and it can also cause accidents.
Below is a link that you may like to watch, at least some of (it is rather lengthy, but it really emphasizes the need to do this wisely! tvnz.co.nz/serious-crash-unit/scu-s6-ep6-v
Diets in themselves aren't a good idea either. They tend be be too restrictive and/or boring at best, and often unhealthy re lack of good nutrition causing a myriad of problems at worst, including fatigue.
Make sure that you are eating enough and don't skip meals, AND that what you eat is nutrient rich, not the quick-fixes of processed carbs and/or high unhealthy fats. It might also be helpful to see a Dr and explain what is going on - it may be that you are iron deficient and might need some supplements.
You also need to address is the amount of work that you do.
Is there some way that you can cut back AT ALL?
Are you able to do your schooling part-time?
Are you doing stuff at home that maybe doesn't need doing so often? (things like vacuuming, etc.)
Are you able to bulk-purchase veges (fresh and frozen) and meat when there are good specials, and then bulk cook them for your meals. It saves a lot of time and it saves money because you take advantage of the specials, and the one lot of power/gas used to cook them. Containerize them in single serves and then freeze them.
Rather than going to the gym, perhaps you might like to think about a few snatches of exercise during the day, rather than adding a further hour or so to your day. You will get just as much benefit without extra pressure.
I hope that you find what works for you.