With that number, I'd think your thyroid might be over-active. Most women feel best with a TSH number around 1.2 - 1.6 or so. Check out http://www.stopthethyroidmadness.com/ for some good information on thyroid problems. Please note that the "normal" range you were given is NOT really normal. That range includes many, many people who are undiagnosed, but have abnormal thyroid function - therefore for many years, the TSH "average" numbers have been extremely skewed. My doctor basically said she almost doesn't care what the test results say, if a patient presents with multiple thyroid malfunction symptoms, she will treat for it until the patient feels better.
ETA: Here's something I found on Stop the Thyroid Madness which may explain both your symptoms and your low TSH value:
"WHAT IS THE TSH??? In your body, the Thyroid Stimulating Hormone (TSH) is synthesized and secreted by your pituitary gland…i.e. it’s a PITUITARY hormone, NOT a thyroid hormone. You can view the TSH like a messenger sent to knock on the door of the thyroid. And its purpose is to regulate your thyroid gland–to tell it to produce more, or to tell it to produce less. In a healthy individual, its message is based on whether your blood levels have too little thyroid hormones to meet the demands of your body, or too much.
When the thyroid gland becomes diseased or disabled and fails to do its job adequately (called hypothyroid), the TSH knocks and knocks on the door, and theoretically, the TSH lab will show a high number. Or, if the thyroid gland gets on its exercise bicycle and overproduces thyroid hormones (called hyperthyroid), the TSH lab will theoretically go low to show that the TSH in your body isn’t knocking.
Occasionally, patients will have a very low TSH with raging hypothyroid symptoms, and that can point to a problem in the Pituitary gland, called Hypopituitary. The latter is usually due to a diseased pituitary gland, or a problem with the Hypothalamus, which is the organ that sends it’s messenger to the Pituitary. (The Hypothalamus, Pituitary and Thyroid glands make up with is called a Feedback Loop.)"