You can register to get access to your medical records online here in UK since this April. All surgerys must comply ASAP (when I asked for access in Mid April I was first patient to do so in our large group practice of about 10 GP's, so I don't think they have been inundated with requests!)
This doesn't give full access, to all notes or letters from consultants (yet at least, it may in future) but it should give access to excellent record of all blood tests (and ranges)
You need to physically go to your surgery with photo ID, fill in a form requesting access and in a few days the surgery write or email you log in details to access your own health records.
Some on here have found their GP practice still not complying with this.
If this is the case with your surgery, you are still entitled to printed copies of your own results, by law. Asking nicely, but firmly often does the trick.
Before trying T3 perhaps you need to find out if your B12, vitamin D, folate and ferratin are well within range. Most thyroid patients seem to need these at higher end of normal for the thyroxine to "work". If these are low the thyroxine (or T3) struggles to be used. Then can feel tired but wired. Exhausted and anxious.
If GP won't do required tests can get privately see Thyroid Uk
Many find going 100% gluten free reduces symptoms, especially if have auto-immune Hashimoto's
As Clutter says, low vitamin D can make legs extremely painful. I have personal experience of that at moment. In my case due to missed diagnosis of gluten intolerance or possible coeliacs (20 years ago was told by endo I did not have gluten issue) So struggled on since on thyroxine with non resolution of many symptoms. Recently gone gluten free and improving. Wish I had tried it years ago Gluten issue has caused me long standing low vitamin D and low magnesium.