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I know what you mean because I gained a few pounds my first year here too for no other than the face that Korean food is SO awesomely good. I suggest that you cut out the big meat dishes especially 삼겹살/고기구이(Korean BBQ of any sort), 양념 치킨(Fried Chicken), 불고기(Seasoned Beef), 탕수육, etc ... and if you want to eat meat a healthier option is 보쌈(Steamed Pork). Also cut out the rice, or at least half it. I think that's what caused my initial weight gain was the heaping bowl they give you and me being self conscious of the restaurant women or my friends saying "Why don't you eat your rice? Koreans eat all the rice!" Now I simply don't care and say that white rice makes you gain. Also it's nice if you can find a regular place which serves 흑미밥 which is the purple/black rice which is A LOT healthier and eaten more-so than white rice in Korean homes. As for the rest of it well .. the main issue with restaurant foods is the salt content, even in seemingly healthy foods such as 김치찌개(Kimchi Stew) or 된장 찌개(Bean Paste Stew) ~ is that it is stock full of added salt ... and asking for it to have less salt isn't going to work as most of the places pre-make their food. But if no other options are available this is much better than meats everyday and cut out the rice! Fill up on the vegetable side-dishes as well. Also sadly a lot of restaurants use MSG. Eating in a restaurant you're never going to get the healthiest meals unfortunately.

I was also a University student in Korea for a year and a half and my University, although a very small one, offered student meal plans and I'm wondering if maybe your University offers this too? or that you could just eat a majority of your meals on campus? They are more "home-made" than restaurant meals and thus much lower in the use of salt/MSG and they are cheap - my Uni. offered meals from between 2,000~4,500원 maximum which was a couple of dollars less than the meals in the public area.

Also, no matter where I have been in Korea (and I have been to some extremely countryside areas) there has been a convenience store/grocery stop/or traditional market at which ready-made food is sold which is a lot healthier than in restaurants. Convenience stores sell small meals such as sandwiches and healthy drink alternatives that you can buy in single meal increments. Some even have salads - but sometimes these are only at the larger ones such as Homeplus/E-Mart.

Traditional markets (I'm sure you have one near you, especially being in the countryside) sell healthy snacks such as 누룽지 (Burnt Rice), or 쥐포 (Dried Fish) and are very tasty. You can also get street foods such as 떡볶이(Spicy Rice Cakes), 파전(Korean Pancake), 찐만두(Steamed Dumplings). - just skip a lot of soy sauce.

Also stock up on fresh fruits! I know they're not the cheapest here but those are good snack/breakfast alternatives.

It's a shame you can't cook or store food because it gives you so many more options. Even when I stayed in a 고시원 which is a cheap as heck one room for mainly students that was the size of a closet there was a dorm refrigerator in it and a shared kitchen downstairs. I can't imagine how you can survive with the only option being to eat outside every single meal.