Feeling discouraged after a week of Intense Effort :/ HELP

You are way under eating.... please read this.

http://www.myfitnesspal.com/topics/show/1080242-a-guide-to-get-you-started-on-your-path-to-sexypants

Weight loss is not a linear process. You are a young, 18-year-old, woman and therefore your weight is affected by changes in hormonal cycles and changes in water retention. In addition, if you are accurately recording what you are eating in your diary, you are not maintaining a proper diet for health with enough calories in it. You also haven't shared how much you weigh, only that you want to lose 25 pounds so I can't tell if you have the pounds to lose without risking your health.

The MOST important thing at your age is to be healthy and eat a healthy diet. Your body will naturally change from a girl's body to a woman's body in the process. Make sure you check with your parents, your doctor, or another health professional to make sure what you are doing is the best for you.

Yes, I weighed 200 lbs. when I graduated high school and had those 25 pounds to lose then. I learned at that tender age that the only way to do it is the healthy way.

If I bump up to 1200 and start eating breakfast every day, do you guys think I'll be able to lose 2 pounds a week?

Whats the rush? I know you (and lots of people) want to lose lots fast. But really you should aim for no more than a pound a week, take a look at that post I linked and figure out your tdee, be honest with how much you are working out and the formulas work. Weight loss takes time, the last thing you want to do is restrict your diet so much that when you try to switch to maintenance you gain most of it back.

Slow and steady..

you should definitely eat breakfast EVERY day, think of it as starting the engine.

people can say what they want about being underfed but unless you are feeling hungry or dizzy everyday your metabolism has already adapted to this lower rate, and the only way to change that is to eat more than you burn for a prolonged period of time, thus causing weight gain instead of weight loss.

It is not necessary eat breakfast in order to lose weight, although that works for many people, myself included. What IS necessary is to eat enough nutritional sound foods to properly fuel your body to function properly and fuel your activity. To lose weight, eat at a slight (300-500 calorie) deficit. So if your body burns, so 2500 calories per day, eat 2000 calories - you WILL lose weight.

Echoing above. You need to be eating a lot more than you are.
Also, be wary of some of the MFP member entries. You're logging pizza, but it's not tracking your carbs, fat, protein, ect; they're all listed at 0. You'll want to be making sure you're hitting your macro targets as best as you can every day.

I used this TDEE calculator (using generic numbers for part of it since I don't know your details), and it says someone like you burns around close to 2200 calories a day including your exercise:
http://iifym.com/tdee-calculator/

Even if my numbers are slightly off, that still means you can eat 1200-1700 calories a day and lose 1-2 pounds a week. I'd go closer to the 1700 a day/1lb a week, because slower weight loss usually results in the weight staying off more easily. It's not a race. Losing slowly is really beneficial in the long run.

Right now you are starving your body. If your body isn't happy, it's not going to give you what you want. Eat more and maybe cut back on the exercise (you don't need to run EVERY day). Good luck.

I have been trying to lose weight since the end of March. Have lost 18 pounds since but haven't lost weight in the last week and a half even though I have been trying harder. I feel discouraged especially since my weight has only stayed the same since I started with MFP. I have been running 2-3 miles a day yet haven't shed weight recently and I don't know why. Perhaps you guys could give me some feedback. My diary is open so check it out

2-3 miles a day can still be easily overcome by calories eaten. 3x7 days a week is about 21 miles. I'm not saying to run more but I was doing 40-50 miles a week last summer and fall (Hopefully this summer too) and at that point I really don't even need to log food other than to check up on macros. Even then I could have easily overeaten if I would have been eating crap all the time. On the flip side I couldn't do that much work without the proper fuel. Don't shortchange yourself.

Check your food intake vs. what you're putting out in exercise. You might be surprised. Don't go under by more than 500 NET calories if you want to lose or over by more than that if you want to maintain. Sudden drastic weight changes aren't good in either direction.