Re: Addison's and MS
Yes, it seems many with Addison's do not convert their T4 to T3, and I'm one of them.
You should start by getting labs of your Free T3 and Free T4. TSH won't tell you much if you're not converting. If you are not in the mid to high levels for T3 and T4, you might benefit from either adding T3, or Armour, which has both T3 and T4 in it.
Many doctors do not want to prescribe T3 or Armour, so you may have to "shop around" if your current doctor won't go there.