Hmmm - I responded to this a couple of hours ago, but I guess my comments didn't post for some reason.
Have you been diagnosed with a thyroid condition? If so, what condition were you diagnosed with? Also, are you currently, taking any type of replacement thyroid hormone medication? If so, what medication/dosage are you taking?
Since you're not taking any thyroid hormone medication, it would appear that you probably need some...
So now to explain what the tests mean... if I tell you things you already know, it's just because I don't know how much thyroid information you actually have, so I'm going to basics.
The thyroid produces 2 major hormones - those are T4 and T3. It produces much more T4 than it does T3. Of the total T4 produced, most is bound by protein so it can't be used. The unbound portion is called the "Free T4" (free meaning unbound and available for use). Free T4 isn't used directly by the body/individual cells. Free T4 converts to, either Free T3 or Reverse T3 (rT3).
Like T4, most of the T3 in your body is bound by a protein and can't be used. The unbound portion is the Free T3 and is the hormone that's used by nearly every cell in your body. rT3 is inert (does nothing), but it can block Free T3 receptors. Some reverse T3 is good/natural, but if more Free T4 is being converted to rT3 than Free T3, we tend to have hypo symptoms (like yours)
Most of us do best when Free T4 is at/about mid range. Yours is good at 58% of its range. In addition, most of us need Free T3 to be in the upper half to upper third of its range. This is where you seem to be having issues because your Free T3 is only at 33% of its range.
TSH is Thyroid Stimulating Hormone, a pituitary hormone that stimulates the thyroid in an effort to get it to produce more hormones. Typically, with a Free T3 as low as yours, plus the symptoms you have, we'd expect to see TSH much higher than yours.
Thyroid Peroxidase is an enzyme used to produce thyroid hormones... The test you had done, should actually be labeled "Thyroid Peroxidase Antibodies" (TPOab). Antibodies are produced when we have an autoimmune condition called Hashimoto's. The antibodies attack and eventually, destroy the thyroid so it no longer produces hormones (T4 and T3). Your antibody count is lower than the reference range, indicating that you may not have Hashimoto's. However, there is another antibody test that should be done that's also an indicator of Hashimoto's. That's Thyroglobulin Antibodies (TgAb). When we have Hashimoto's, we will eventually become hypothyroid because our thyroid can't produce the hormones we need.
These hormones control metabolism, body temperature, heart rate and many other body processes.
Typically, with hypothyroidism TSH is higher than normal because the pituitary (called the Master Gland) is calling for more hormones, but the thyroid doesn't respond, so the pituitary keeps producing TSH in an effort to get the thyroid to respond. Sometimes, however, something happens to the pituitary or hypothalamus (another gland in the brain) and it doesn't put out enough TSH to stimulate the thyroid... In these cases, there's nothing really wrong with the thyroid, it's the pituitary that's malfunctioning. This is called Central (or Secondary) hypothyroidism. Many doctors will misdiagnose someone with Central/Secondary hypothyroidism because the TSH is low and often, that's all they look at, even if they order Free T4 and Free T3 along with it.
In addition, some people have problems converting Free T4 to the usable Free T3. Since your Free T4 is more than adequate, but your Free T3 is quite low, I'd think you either have Secondary hypothyroidism or a conversion issue (Free T4 not converting to Free T3 or converting to too much rT3).
My suggestion would be to request the other antibody test (TgAb) to help rule out Hashimoto's and ask for Reverse T3 (along with another Free T4 and Free T3 since they need to be done at the same time), which is a hormone that mimics Free T3 - it's a mirror image.
Also, if you've been tested for Vitamin B-12, Vitamin D and ferritin, please post results with reference ranges. Many of us with hypothyroidism are deficient in all 3. Vitamin B-12 and D are necessary for the metabolism of thyroid hormones. Ferritin is the iron storage hormone, which tells how much iron we have in store. Iron is necessary for the conversion of Free T4 to Free T3. If you haven't been tested for these vitamins/mineral, please ask your doctor to order them.
I'd also suggest that you ask for a thyroid ultrasound to determine whether or not you have nodules on your thyroid. Many of us do and most of the time they're no problem, but if they exist, they should be monitored.
I hope this helps and if I confused you, please feel free to ask for clarification. :-)