Thyroid meds take A LOT of tinkering. I agree that strong side-effects are a sign that a medicine doesn't work well with your bodies chemistry. That said:
I've taken Synthroid (t4), Armour (T3/4 combo) & Cytomel (T3 only). The worst side-effects I've ever had on ANY medication,
in my entire life, were 7 weeks I took Synthroid.
(Also know many, MANY people who swear by it) Personally, I feel a LOT more like me

when I'm taking a thy med that has T3's IN it.
Glad your Doctor is open to letting you try Armour

I left a Dr of 4+ years who wouldn't take me off synthroid,
knowing I was having HORRID side-
effects,,,