You have been diagnosed with hypothyroidism
and started on treatment accordingly. In patients with hypothyroidism the dosage of medicine is titrated based on your subsequent TSH
and T4 levels. Since you have just started treatment you will need to repeat your tests after 6 weeks. If this report is normal ( to be decided by your physician ), then further tests are done once in 6 months. If the dose needs to be changed, more frequent testing is required.
As for your second question, at present the only treatment for hypothyroidism is to take thyroxine
Hope that answers your query.