Holly_cg As you were only diagnosed in March, you should still be in that period where your GP should be testing your levels every 6 weeks or so and adjusting your medication. This should continue, test, increase meds, re-test, every 6-8 weeks until your symptoms subside. Changes in dose take a few weeks for the effect to be felt so we have to be patient, particularly when newly diagnosed and trying to find the correct dose.
Your test result above, TSH 16.2, show that you still have a long way to go. Generally, in a medicated hypo patient, the aim is to get TSH to 1 or below or wherever it is needed for the FT4 and FT3 to be at the top of their ranges and you feel well. If your doctor thinks that is normal then he ought to be in a different job as he knows very little about thyroid.
As for your vitamins and minerals, Ferritin is way too low, it should be half way through range. You need to supplement iron, take it 4 hours away from thyroid meds because it affects absorption of your thyroxine, and take with 1000mcg Vit C to prevent constipation and aid absorption.
Your B12 is very low. The Pernicious Anaemia Society recommend a level of 1000. Supplement with Solgar or Jarrows sublingual methylcobalamin lozenges, 5000mcg until your level is optimal then reduce to 1000mcg as a maintenance dose.
You need to check the range for folate, I think you've got the upper end wrong. Whatever the range, folate needs to be at least half way through. If you supplement with B12 you should also take a B Complex to balance the B Vits. If you get Thorne Basic B it contains 400mcg folate which will help improve your folate level.
It would be a good idea to get a Vit D test. Either ask your GP or get one done privately, £28 through City Assays, which is a blood spot fingerprick test.