Firstly, this has been radically simplified as multiple mechanisms can be simultaneously at play and they can't all be addressed here
Firstly why do you think you need iron tablets? Is it because your INR or PTT (blood clotting time) is high due to drinking and your red blood count is possibly on the low side? Usually this has nothing to do with iron levels but as the Liver is the organ that rids the body of excess iron (amongst other dangers) via feces, once the Liver is compromised iron gets stored in remaining tissues and creates an increasingly toxic environment that continues to stress and do damage to what remains of your Liver (it substantially increases the risk of liver cancer up to 10 times). Add to this an important piece of information: your liver produces blood clotting factors so cuts or surgery become real issues if your INR is higher than 1.5 (normally 0.9 - 1.2). Again this rarely has anything to do with low iron levels in heavy drinkers.
You will have to see a doctor to get your blood tested where they will test for high iron levels by testing serum ferritin which will give a measure of total iron stores. If iron levels are high it is called hemochromatosis and can be treated traditionally via blood letting or more recently with medication. Be honest with the Doctor about how much you drink as it will affect his/her decision making. Lying might be less embarrassing than admitting the truth but is it worth shortening your life to spare yourself minor embarrassment?
if I sound preachy, sorry but I am at the other end of liver failure and it's a really unpleasant way to go.
Good luck with it all
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