Normal range for TSH is considered to be 0.3-3.0, so yes, your level is below range; however, if TSH is the only thing tested, that's not a good picture of what's really going on. You also need to get the actual thyroid hormones, Free T3 and Free T4 tested.
Do you have symptoms of hyperthyroidism? If so, which ones? Have you previously been diagnosed with a thyroid condition? Are you on any type of thyroid medication? If so, what med(s)/dosage(s)?
Since about ten years ago, recommended reference range for TSH according to AACE is 0.3-3.0...below 0.3 indicates possible hyper, and above 3.0 indicates possible hypo. So, yes, the nurse is right.
TSH is volatile, varying significantly intraday, so it is, at best a screening tool. Many things can affect it besides thyroid hormone levels. What your TSH really indicates is more testing. FREE T3 and FREE T4 (different from total T3 and total T4, which are not nearly as useful) will tell you your actual thyroid hormone levels. TSI is an antibody blood test.
TSI (thyroid stimulating immunoglobulin) is the definitive test for Graves' disease, which is almost synonymous with hyperthyroidism.
Your doctor might also want to run two other antibody tests...TPOab (thyroid peroxidase antibody) and TGab (thyroglobulin antibody). If either of these is elevated, Hashimoto's thyroiditis can be indicated. While Hashi's is eventually a hypO disease, early stages can be characterized by hyper phases.