Is losing weight under a month without exercise and an increase in appetite normal?

Need more details: You need to tell us what your usual/normal weight is(over last 6 months) and how much weight you have lost? You should record your weight in a diary and do so daily or once weekly over 2 months. If you lose more than 2-3 pounds over this period of time, you should get checked by a physician. One likely cause is an over active Thyroid gland. This can be easily verified with a blood test(TFT).