The general rule of thumb, and has been for some years now, is not to go below 1200 calories for women. I would at least bump it up to that, or you do run the risk of burning muscle, slowing your metabolism, and triggering your body to hold on to fat. These are all very real scenarios that could make losing weight a lot more difficult than it already is lol...
Yes, you will tend to feel more hungry when you are working out, because that work-out is taking liquid out of you (so drink plenty of water!) and burning even more calories.
Just my opinion would be to raise your calories to at least 1200 on the days you don't work out and 1400-1600 on the days you do work out. I personally think 3 lbs is a bit fast to be losing per week at your size (since you aren't significantly obese or anything). It feels really good when the weight comes off, but research has shown that people who lose a bit slower (1-2 lbs per week) tend to keep it off longer.
Try that for a couple weeks, and tweak as necessary.
Good luck!