It is possible for the thyroid gland to start functioning normally again, and for you to not need the thyroxin again. However, you need to take the following precautions:
1. One month may not be sufficient time for thyroid function tests to become abnormal. You should repeat T4 and TSH again after 1-2 months, to make sure.
2. It is a good idea to get thyroid function tested every year. You can get T4 and TSH tested, or even just TSH alone. Till the time the tests stay normal, you do not need to start thyroxin.