Triiodothyronine also is known as T3 is the active form of thyroid hormone.  T4 also known as thyroxine is made in the thyroid gland.  T4 is then sent peripherally through the system, and mainly the liver will convert T4 to T3.  You can have all the T4 in your body, but if your T3 is low, then you will have symptoms of low thyroid.    
If suspecting a case of low thyroid, thyroid disease, hypo or hyperthyroid your conventional doctor is going to run a TSH blood test.  The TSH (Thyroid Stimulating Hormone) is a signal from the brain monitoring thyroid disease and the thyroid levels in the body.  
To put it simple:  

If the thyroid levels are high, then the TSH is low.  
If your thyroid levels are low, then TSH is high.

As mentioned above the thyroid mainly makes T4, which is released into the blood and will travel in the body and be converted to the active form of thyroid, T3.  Approximately 60% of this conversion occurs in the liver, about 20% is converted by gut flora and about 20% is converted by peripheral tissues, such as muscle.  

As we have always talked about before, your primary care doctor is looking for a ‘disease.’  If you have a ‘disease,’ your GP, internist, or endocrinologist can save your life.  In the case of thyroid, your conventional doctor is going to run a TSH and perhaps a T4.  That is because they are looking for thyroid disease, not low levels of T3.   
Many people with Low T3 get missed by their doctor because their TSH is in the normal range.  They are told, “you are fine,” even though they do not feel fine.     

How do you know if you have Low T3?  You can do a blood test for Free T3.  Free T3 is the bio-available thyroid hormone ready for use.  In checking for Low T3, you want to check the free T3 levels, not the Total T3 levels. Total T3 levels in the blood represent all Free T3 and bound T3 levels.  Testing for total T3 levels is not going to be accurate enough to find out if you have Low T3.

You may need to request blood testing for Low T3 from your doctor, or you may need to order it yourself if your doctor will not order it.  
Blood tests checking for Low T3 Level:


TSH
Free T4
Free T3

This is where it gets a bit confusing.  The reference range for Free T3 is broad.  

Free T3 Reference Range:


2.3 to 4.4 (depending on the lab).  
If your Free T3 is under 3.0, we would consider this to be a Low T3 level.

Testing results we commonly see in patients with Low T3:


TSH: normal range usually between 1.0-3.5 (reference range is .45-4.5)
Free T4: 1.1-1.4 (reference range is .8-1.8)