Hashimoto's and Wilson's Syndrome at the same time?

i have been diagnosed with hashimoto's hypothyroidism and after a year of treatment, nothing is working. the docs now say i have chronic fatigue syndrome, and possibly lyme disease. anyway, i don't think the synthroid is working, but armour didn't work either. my question is, can you have hashimoto's and wilson's syndrome together or is that not possible? i'd like to look into the t3 therapy but not if it won't help hashimoto's. thanks!