Also know that properly balancing Thyroid hormone may itself bring your Cholesterol into proper balance. High cholesterol is a symptom of being Hypo. Most Dr's seem not to know this.
I don't think Armour should cause heartburn, but fish oil most certainly will if not taken with a meal or lots of water - at least it does me.
Do you take all of your Armour at one time? Many people on desiccated medication find that it works better if they split the dosage, with 1/2 first thing in the morning, the other 1/2 around noon or so. This helps keep the T3 more even throughout the day.
Always be sure to separate thyroid medication from vitamins, minerals or herbs by at least 4 hours.