I think you should look more closely at your hashimotos and synthroid supplementation (I'm also a thyroid "patient").
For example, I recently found out that synthetic thyroid is bad for people who are already adrenally compromised (and I suspect you are, given your parasite infestation); and in fact it can aggravate the already compromised adrenals. I am beginning to realise how important it is to address adrenal insufficiency by supplementing with vitamin B5, vitamin C and various adaptogens (for example astragalus, ginseng) and to reduce taking the synthetic thyroid meds. Hvergarthi is really good on adrenals so you might like to visit the adrenal board and look through his posts. B5 is also indicated for R Arthritis as well did you know?. These are a few good things for you to consider.
IMO and personal experience thyroid is far better supported with Iodine by taking iodoral or Lugols drops. Its so important, trust me. I have a feeling that the synthetic hormones destroy the thyroid even further and can cause all sorts of other issues, for example heart palpitations and racing.
I have personally gone down from 200 mcg, to 100 mcg to 50 at the moment. I'm going to get off this stuff and build up my adrenals instead.
BTW Dessicated thyroid extract is much better for you than the synthetics if you can find a doctor to put you on armour thyroid instead of the synthetics. Synthetics are only in the current picture because of the pharmaceutical companies wanting to cash in on our misery :-(. Our mothers and grandmothers were on the natural stuff with great success; but sadly the docs like giving us synthetics and its only a matter of time before your body rejects it.