Lots of good advice here for you, OP. Hopefully it will make you feel reassured regarding some of your symptoms.
Naturally, you'll be eager to feel lots better, but after taking your first lot of pills prescribed for only about 4 weeks, it may not be surprising to find that your next blood test could show that the dose needs some tweaking/changing in order to bring about some real improvement. Patience may be needed for a while!
Meanwhile always remember to take your Levothyroxine with a glass of water a good half an hour prior to any food or drink (first thing in the day). Calcium, for example, will interfere with absorption, and eating or drinking could easily affect the performance of the dose you are prescribed. Secondly, because your whole being is regulated by the workings of your Thyroid, don't be dismissed or feel that your comments or complaints about this aspect of your health are not being given adequate attention by your GP. Making your own appointment to see an Endocrinologist would probably be of great benefit to you if you feel that this is a health problem which, for you, needs more support or investigation - and especially if you continue to feel unwell or constantly out of sorts.
A few years ago, I spent some months suddenly feeling absolute rubbish and couldn't understand why. The levels of thyroxine were correct according to the results of my latest blood test. I eventually complained to my Doctor and asked to be put onto different medication, amazingly on the very day that the French Government had started action against the drug company producing their generic Thyroxine tablets. Thousands of French women had been raising hell with regards to how their tablets were affecting them - as a result of unknown additives/fillers/bulking agents having been added to those particular pills. These random additives were what was affecting the dosage AND the results for patients. The drug company had omitted to inform the Government bodies responsible and therefore Doctors did not have the information either! I was put onto a completely pure (Thyroxine + Water) capsule by an Endocrinologist and have never looked back.
I hope that with a bit more time you will benefit from positive improvements in your condition.