"The t3 and t4 both are below 0.4." What are the exact results and reference ranges? And are they Free T4 and Free T3 or are they Total T4 and Total T3? They aren't the same tests and don't provide the same information...
Your symptoms indicate hypothyroidism. Hashimoto's is the # 1 cause for hypothyroidism in the developed world, today.
As noted above, it takes approximately 4-6 weeks for the medication to take full effect, but you may see some slight improvements before that time. The body heals the most important systems first, so if there are other things you aren't noticing, such as low heart rate, etc. those may be corrected before any weight loss or muscle joint pain will be alleviated.
Have you been tested for Vitamin B-12, vitamin D or ferritin?
I'd suggest you ask for antibody tests, the vitamin tests and a thyroid ultrasound as soon as possible.
I haven't personally had TSH that high but we've had members on the forum in the past who have. Although that's very high, TSH isn't the main thing to worry about. The most important thing(s) are Free T4 and Free T3, which are the actual thyroid hormones and of course, symptoms.
With TSH over 500, we would expect Free T4 and Free T3 to be very low and for the patient to be very ill. We'd expect them to be started on thyroid hormone medication immediately and although it takes several weeks for the medication to reach full potential, it's possible for some relief of symptoms rather quickly, but that depends on what symptoms and the severity.
It would probably work better if you tell us about your situation since I don't know of anyone, currently, on the forum who has TSH that high. Please also post other test results (Free T4 and Free T3, antibodies, etc) and reference ranges so we'll know what's been done and what's still to be done...