What is the initial dose of Synthroid you are on?
Good that you are now on brand name Synthroid and not on generic, it takes at least six weeks for the medication to become effective, this is because half life time of Synthroid (T4) is one week and thus it takes at least six weeks for the amount in your body to reach about 98%, in addition to that it is important to know that with hashimoto's you most probably will need to increase your dose of T4 several times, each time you increase the dose based on TSH your TSH will drop a little in six weeks, depending on how much you have increased, in an another six weeks it might climb again indicating the need for an another increase, until your levels remain stable, this should be a process and each one of us with hashimoto's has to go through it.
Adding T3 to T4 medication does not help according to all big studies despite that some people say that they feel better, this is according to my ex-endo, so it is very likely that you do not need the T3 medication, it is very possible also that you are on a high initial dose of T4 than what your TSH allow.
As for Armour, there are many things to consider before switching to it, first thing is that it is not approved by the American FDA, it contains both T3 and T4 but because it is made from powdered porcine glands the ratio of T3 to T4 in it differs from what humans need and it is generic in addition to all of that, NDT is what was used before synthesizing T4 in the laboratory .
Best of luck and good health,