Your levels are pretty dire to be honest. Iron deficiency can cause heavy periods so it's more likely the other way around. You need a full blood count and iron panel for iron and folate/b12
Your B12 is extremely low and I would suspect deficient and ranges used are out of date and needs to be investigated as B12 can cause irreversible neurological damage. You can ask on the pernicious anaemia forum on here for further advice.
In my personal opinion, I would stop the folic acid until B12 is resolved as folic acid can make B12 deficiency worse and acerbate B12 deficiency.
In regards to vitamin d - 800mcg is just a maintenance dose - you need much higher dose than this,
Is there any reason why your levels are so low as you are clearly absorbing nothing if you've been on iron for that long - do you eat enough and healthily enough, do you have any digestive issues?
As SaggyUK said, your levels are pretty bad. They really need addressing for your thyroid treatment to work properly.
For me, sublingual sprays were the way to go for B12 and D3 as they bypass any absorption problems you're clearly having by taking supplements in pill form.
Your doctor may or may not agree to give you B12 loading dose injections (mine did, but then refused to continue B12 injections thereafter, but I've managed to keep my B12 above 800 with the spray. The lab reference range in the UK is incorrect and many people are symptomatic when B12 goes below 500 (I am one of those people).
You want your vitamin D level to be at 100 or more, and 800iu supplementation is fairly useless for most people. I take the 5000iu spray every day and maintain mine at around 120-130.
I can't really comment on the ferritin apart from to say yours is EXTREMELY low and most people on these boards are in agreement that thyroid treatment is never optimal unless ferritin is up at 70 or above. I think that area definitely needs research as it's so low and you've been supplementing (to apparently no effect) for so long.
I just googled 'iron absorption problems' and one website told me: "Diseases conditions can also limit iron absorption; this can happen as a result of insufficient stomach acid, lack of intrinsic factor (hormone needed to absorb vitamin B12), celiac disease, inflammatory conditions such as Crohn's disease, and in autoimmune diseases and hormone imbalances."
Leaving aside the autoimmune and hormone conditions for a while, have you ever been checked for coeliac disease or pernicious anaemia (that's the intrinsic factor one)? Have you ever tried going 100% gluten free? Since you have trouble absorbing everything you really need further investigation. If it's just low stomach acid you can do something about that easily. However your doctor should be investigating other possibilities. Do you have any symptoms that are not normally associated with hypothyroidism e.g. stomach pain?
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