In trying to diagnose a potential thyroid issue, by far the most important is an evaluation for the existence of multiple symptoms typical of hypothyroidism. So before further discussion, please review the following list of symptoms and tell us which ones you have, if any.
Fatigue
Increased sensitivity to cold (temp. below 98.6 which is considered normal)
Constipation ( have to use fiber or laxatives)
Dry skin (have to use moisturizer)
Weight gain
Puffy face
Hoarseness
Muscle weakness
Elevated blood cholesterol level
Muscle aches, tenderness and stiffness
Pain, stiffness or swelling in your joints
Heavier than normal or irregular menstrual periods
Thinning hair
Slowed heart rate
Depression
Impaired memory
Enlarged thyroid gland (goiter)
insomnia/sleep apnea
Well.
The first question is how do you feel?
Because if you feel fine. The numbers are about meaningless.
Have you looked and do you have any of the common symptoms of low (or high) thyroid?
Some general thoughts. #1 TSH is at best a screening test and mostly worthless unless it is pretty far outside the range high or low. And if a person is on thyroid me, it becomes even less valuable.
In general the lab ranges are too low. And it is very common for people to have symptoms while they are low in the range but still in the range. Which means Dr's will do nothing for you expect tell you that "you are normal" and that anything you are experiencing is either in your head (which they will be happy to throw you some anti-depressants like candy. but will be unwilling to give you thyroid medication.
Another common problem is your Dr has a good chance that he or she will ONLY look at the virtually useless TSH test. and since yours is within range they will look no further. See comment above where they will tell you that you are normal and any symptoms are NOT thyroid related.
In general terms you look low thyroid and I would suspect you may have low thyroid symptoms. While the Free T3 is in range it is very low in the range. lower than many people will feel well at. But everyone is different and feels well at different levels.
I won't go into any more detail until you respond with how you are feeling and why you or your Dr decided to have thyroid panel tests run.
I will give your Dr credit for one thing which is a very good sign. They did actually order the right thyroid tests. Many people have to beg and plead and through a fit in order to get their DR to order a Free T3 test.
With the additional info you gave us, it is important to note that "the effect of alcohol on the Hypothalamus /Pituitary axis is significant and alcohol consumption affects almost all aspects of the functioning of the thyroid gland."
So yes, your thyroid levels (FT4 and FT3) are low in their ranges and lower than most people seem to need. However, rather than considering thyroid medication at this time, you could give your abstinence a chance to get your thyroid system back to normal and see how you are feeling at that time. Personally I would not want to take thyroid med if it were possible to get my thyroid process back to normal.
Also, with those symptoms it would be a good idea to test for Vitamin D, B12 and ferritin and supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper part of its range,and ferritin should be at least 100.
Stay strong and let us know how you are doing.