Is there a different GP you can see. This one is incompetent
What has been prescribed for your very low ferritin?
Have you had full iron panel?
Would recommend getting full private blood tests done
For full evaluation you ideally need TSH, FT4, FT3, TT4, TPO and TG antibodies, plus vitamin D, folate, ferritin and B12 tested
Private tests are available
Medichecks Thyroid plus ultra vitamin or Blue Horizon Thyroid plus eleven are the most popular choice. DIY finger prick test or option to pay extra for private blood draw. Both companies often have money off offers.
All thyroid tests should be done as early as possible in morning and fasting. This gives highest TSH, lowest FT4 and most consistent results
Link about antibodies
Link about thyroid blood tests
Print this list of symptoms off, tick all that apply and take to GP
Vitamindtest.org.uk - £28 postal kit If just want vitamin D test
Detailed supplements advice from SeasideSusie here on similar levels