Before further discussion, please tell us about all the symptoms you have. In trying to assess thyroid status, symptoms are actually more important than test results. Also, please verify that the Free T4 result is .94, not .094. Also, please post reference ranges shown on the lab report for those results.
Why do you say you typically swing between hyper and hypo?
Your doc was probably telling you that you swing both ways, hyper and hypo, just based on your TSH results. They tend to believe that TSH is all that is needed to determine thyroid med dosage. That is very wrong. A hypothyroid patient taking thyroid med adequate to relieve hypo symptoms usually find that their TSH becomes suppressed. That does not mean hyperthyroidism, unless the biologically active thyroid hormones (Free T4 and Free T3) are excessive. Your FT4 was only at 28% of its range, and you were not tested for Free T3, only Total T3. In the future you should insist on always being tested for both Free T4 and Free T3. Free T3 is the thyroid hormone that is metabolized by all the cells of your body to produce needed energy. It is very important to know FT3 level.
Your Total T3 level was above range, which made me wonder if you took all your daily dose before the blood draw for those tests. If so, that can cause a false high result. The morning dose should be deferred until after the blood draw for thyroid tests.
So, again, please tell us about all the symptoms you have had. Also, what dose are you taking currently?
Besides a free T3 as suggested above, I would suggest a reverse T3, especially if taken during the time when you are feeling "hypo" as this could indicate a conversion problem which may possibly be why you swing back and forth. This can be intermittently brought on by stress or other health issues.
Also, swinging between hypo and hyper is also common in those with Hashimoto's. Have you had labs to test for antibodies? If not, that would definitely be something to rule-out.
So with RAI after Graves' I expect that you have no thyroid gland function now and are totally dependent on replacement thyroid hormone medication. As a daily replacement amount, 2 grains of Armour is equivalent to about 132 mcg of T4, and is not a huge amount. Your symptoms of constipation, hair loss, and low metabolism are frequently related to hypothyroidism. Although frequently misdiagnosed as hyper, heat intolerance can also be a symptom of hypothyroidism. Note the following section taken from a very long list of hypothyroid symptoms.
Low basal body temperature (below 97.8 degrees Fahrenheit)
So I expect that your doctor looked at your low TSH and heard your complaint of heat intolerance and decided it must be due to over-medication. In addition I expect that the high Total T3 result also affected the decision to reduce your dosage of Armour. Unfortunately you take your thyroid med in the morning before the blood draw for tests. That can lead to false high results, especially for T3 tests since it affects serum levels quickly. Even the AACE/ATA Guidelines for Hypothyroidism recommends deferring morning thyroid med until after the blood draw.
So it seems that you needed an increase in daily dosage, not a reduction in dosage. In addition, using different doses on alternate days tells me the doctor doesn't understand how fast T3 works. It would be okay if only T4, but not T3. With Armour you should try to use the same dosage every day. Since T3 reaches full effect in about 3-4 hours, some people even split their dosage and take half in the morning and half in the afternoon on the theory that it helps even out the effect over the day.
A good thyroid doctor will treat a hypothyroid patient clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important not just test results, and especially not TSH when already taking thyroid med. This goes against the training and treatment protocol of most doctors but there is more than adequate scientific evidence to support clinical treatment. If you want to read about it, I recommend reading at least the first two pages of the following link, and more if you want to get into the discussion and scientific evidence for all that is recommended.
Hypothyroid patients are also frequently deficient in Vitamin D, B12 and ferritin. So, you should get those tested and then supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end fo its range, and ferritin should be at least 100. If your doctor resists testing for Free T3 and these additional tests, and doesn't agree with clinical treatment then you might consider giving him a copy of the link, to try and persuade him to reconsider your dosage, and consider doing the additional tests, and also clinical treatment. If that doesn't work then you will need to find a good thyroid doctor that will do all this. In that case let us know where you are located and perhaps we can suggest a doctor that has been recommended by other thyroid patients in the area.