I don't think you're eating enough.
Most people your height could lose weight eating about 1500 calories per day. I lose weight eating 2100 per day and I don't even exercise.
Especially with exercise, you should probably be eating more. 1200 is supposed to be a minimum but your body might need more than that. You don't want to start losing muscle mass... and it's possible your body is just building and then burning that.
I'd say, go see your doctor if you can, and just check in about your diet and exercise.
All that said: It's only been a week, and water retention can definitely last that long. I fluctuate a lot from day to day (see graph below)—sometimes as much as 6 pounds in a day—but my weight is trending downwards. You won't really be able to tell what's working until you've kept it up for over a month, and preferably 3.
Best wishes and I hope you find the best healthiest option for you.