It does take 4-6 weeks for dosage changes to take effect. In addition, I would hope that your doctor started you on a lower dose than you really need in order to build your levels slowly and give your body time to get used to having the hormones again.
Typically, you should be tested every couple months, at least until your actual thyroid levels come up and your symptoms are alleviated.
As Christine said, you should take your medication first thing in the morning, on an empty stomach, then wait at least 30-60 minutes before eating. It's true that calcium can inhibit absorption of thyroid med, however, if you typically eat cereal with milk for breakfast, I don't think you need to stop; it might simply mean that your dosage may end up being a bit higher in the end. The main thing is to not take calcium supplements for at least 4 hours after taking your medication.
If you decide to get a referral to an endo, make sure you get one who specializes in thyroid, as not all endos do; many of them specialize in diabetes and are not good with thyroid issues at all.
All of that said - is TSH the only test your doctor is doing on you? TSH is a pituitary hormone and is not indicative of thyroid hormone levels, since it fluctuates for a variety of reasons; anyone being treated/dosed based only on TSH levels, is in for a long hard pull.
You need to have your actual thyroid hormone levels tested - that would be Free T3 and Free T4. Those are the active hormones and tend to correlate much better with symptoms, than does TSH.
If you have other test results, please post them, along with the reference ranges, which vary from lab to lab, so must come from your own report. If your doctor is only testing TSH, please insist that he also do FT3 and FT4.
Do you know if you have Hashimoto's?
I have hypothyroid too. It does take awhile to balance your thyroid with meds. It can take up to 4-6 weeks easily everytime the doctor changes the dose. Are you seeing an Endocronologist for that? If not get your doctor to refer you to one. They specialise in the thyroid gland. Good luck. Smileyhappy.
It can take a while for your body respond to the medication. Normally, your doctor should do another blood test about 4 weeks after you start your medication to check your levels and see if a dose adjustment is needed. Until you are stable on your dose, your doctor needs to run tests regularly. Eventually you may only need to test 1 or 2 times a year.
Make sure you are taking your medication as directed. I take a generic version of Synthroid. I have to take my med 1st thing in the morning on an empty stomach. I have also read that calcium (such as from milk, cheese, etc) can interfere with absorption so I do not eat or drink anything high in calcium for two hours or so before or after I take my medication.