It is good that the doctor is willing to test for both Free T4 and Free T3. Make sure to ask the lab person who draws your blood for the test, which tests are to be done. That way you can make assure it is Free T4 and Free T3, not Total T4 and Total T3. Also, even though Hashi's most often shows with the TPO ab test, it sometimes shows up with the TG ab test, so that should also be done. Please keep in touch and let us know how you are doing.
In assessing a patient for potential thyroid problems, the most important consideration is symptoms. Next is a comparison of the biologically active thyroid hormones, Free T4 and Free T3, test results to their reference ranges shown on the lab report. You were only tested for Total T3 and Total T4, which are not nearly as revealing as the Frees. So in the future you should make sure they always test for Free T4 and Free T3 each time you go for tests. Lacking Free T4 and Free T3, we can have a look at the Totals, so please post the ranges for the Total T3 and Total T4.
Your TSH is above range and high enough to be considered overt hypothyroidism. It may also be an indicator of the main cause of primary hypothyroidism, which is Hashimoto's Thyroiditis. With Hashi's the autoimmune system erroneously identifies the thyroid gland as foreign to the body and produces antibodies to attack and eventually destroy the gland. As this proceeds, the output of the gland is reduced and the pituitary produces more TSH in an attempt to stimulate more thyroid hormone production. So you need to be tested first for Thyroid Peroxidase antibodies (TPO ab), and if negative, then test further for Thyroglobulin antibodies (TG ab). Hashi's usually shows up with the TPO ab test.
With no symptoms, a high TSH, and probably TT3 and TT4 within range, it likely indicates early stages of Hashi's. So the doctor may choose to do nothing for now. If it is Hashi's, you will eventually begin to develop symptoms and need thyroid medication to offset the loss of natural thyroid hormone, and relieve hypo symptoms.
In that case, you will need a good thyroid doctor that will treat clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just lab results. Being an Endo does not guarantee that he will be a good thyroid doctor for a number of reasons. So I suggest that when you see the Endo, you should ask if he is willing to treat a hypothyroid patient clinically, as described. Also ask if he is willing to prescribe T3 type meds like Armour Thyroid and NatureThroid. If either answer is no, then you will need to find a good thyroid doctor elsewhere. Being in India, if you need T3 in your meds, that too is a problem for you.
We can provide a lot of help to you as you go forward with all this. There is much knowledge and experience on this Forum that we will be happy to provide. Please let us know if you are able to get the Free T4 and Free T3 tests done, and also the TPO ab and TG ab. Also please keep in touch and let us know what the Endo says about all this.