What Causes Elevation In TSH Levels Despite Having Synthroid And Armour Thyroid?

I m 50yr old female with hypothyroidism/Hashimotos.I have struggled with taking Synthroid and now Armour Thyroid.TSH elevated to 6.10 but T3 and T4 in normal range.Doctors have consistently tried to increase dosage based on TSH. Each time I feel ok for around 3-6 months then I begin to have hyperthyroid symptoms in spite of labs not being indicative of hyperthyroidism. During these periods T3 and T$ still in normal range but TSH always elevated between 4.5-8.1.My dr. directed me to stop taking the 15mg of Armour for a full month and also sent for me testing for Pheochromacytomas (adrenal tumors) which I understand is a very rare condition. Any ideas?