That is a very small dose of levothyroxine. Because T4 is an inactive storage hormone with a long half-life, you shouldn't expect to see any improvement for up to 2 months. The symptoms you mentioned are all hypothyroid symptoms.
There is the tendency to take a medication and then over-scrutinize (we all do this), attempting to match symptoms with the drug itself. With hypothyroidism especially, the symptoms are more coincidental to a dose taken than cause-and-effect, especially at such a low dose.
However, there are some people who seem to have allergic responses to fillers and binders in levothyroxine specifically. Ironically, while most doctors will tell you that T4 drugs are highly reliable (potency and stability) and natural desiccated thyroid products (NDT) aren't, this is simply untrue. T4 drugs are sensitive to heat and moisture and have a long history of recalls (especially synthroid, which was almost pulled off the market in the US)
Most doctors prescribe T4 because they've been told it will convert to T3 in the body. Unfortunately, that's not true in some people, who either have a genetic inability to convert adequate amounts or because they have a tendency to convert T4 into Reverse T3, which blocks the receptor, making you feel even worse. Another reason doctors DON'T want to give T3 is that it's more difficult to dose, as it has a shorter duration of action, and you'll have to take it anywhere from 2 to 4 times a day. In pharmacy, we know that the more often a patient has to take a drug, the more likely they'll skip doses. The final reason why doctors prefer to prescribe T4 drugs, even though these drugs have been proven not to work for certain individuals, is that they accept the 'opinions' of endocrinologists, who have long been the lush target of drug manufacturers' levothyroxine propaganda.
Since nobody has ruled out that you're a non-converter, you'll want to find a doctor who is willing to give you a trial dose of desiccated thyroid. A good starting dose is a 60mg tablet, which will contain 38mcg of T4 and 9mcg of T3. So how do you get the doctor to do this?
When you ask, ask like this..."I want a trial dose for the next couple of months...what harm can that do?" When he starts to babble that strange endo-speak, ask him this: "Is there something you're afraid might happen if I used desiccated thyroid and my symptoms went away?"
Here's the thing: Some of us have read a lot of books on hypothyroidism and so we're the more educated individual in the room. But knowledge doesn't equal persuasion. That's a different skillset. You can take the pressure off the doctor's ego by "ruling something out", rather than forcing them to defend their own mythology.
Most likely you'll have to change doctors. I would estimate that 85% of all medical practitioners will NEVER prescribe natural desiccated thyroid and will try to bully or intimidate you. And even if you do find one who will prescribe NDT, the odds that they'll use the TSH test exclusively to treat your symptoms is even higher. The TSH tends to be suppressed when you've reached an adequate dose, but you'll never get there because they won't violate the TSH rule (0.35 - 4.5, more or less).
So put more of your energy finding a doctor who will:
A) Prescribe NDT for several months, increasing the dose regularly during that time and who will ASK about your symptoms or will listen while you discuss them.
B) Run more valuable tests such as the FREE T3, FREE T4, REVERSE T3 and the Hashimoto antibody tests. They should know the difference between suppression of the TSH (0.03 but no symptoms) and HYPERthyroid symptoms because the dose is too high.
C) Rule out that you have a deficiency of magnesium, iron, selenium, B12, etc. This should occur PRIOR to beginning thyroid hormone therapy. You can have a healthy thyroid gland and still have "low thyroid function".
D) Check for adrenal insufficiency (don't use the word adrenal fatigue...they laugh at that) by using the 4 point adrenal saliva test. This should also be done PRIOR to beginning thyroid hormones because low cortisol will impede your ability to reach a proper dose.