Do you have any nodules? Have you had an ultrasound? I was having hoarseness and swallowing troubles, and I had four large nodules...had a lobectomy to remove the three in my right side of the thyroid, I have not had my swallowing troubles and my voice is great...but we found cancer so I have to have the other side romoved...bummer. You should have an ultrasound to check for nodules...they are usually not cancerous, but may be the source of your troubles.
How much levothyroxine are you taking? The reason I ask is that your free T4 is over the high limit and could be contributing to your symptoms. What criterion did the doctor use to decide on your med dosage? What was the doctor's reaction to your free T4 result?
To better assess what is going on, you need to be tested for free T3 also, since free T3 is the most active thyroid hormone ( four times as potent as free T4). This will give you a much more complete picture of your thyroid state.
In searching for scientific studies that validated which thyroid test correlates best to the variables we are trying to affect, I have found that the very best correlation to hypothyroid symptoms is with free T3 levels. Free T4 is a distant second in priority, and TSH is almost insignificant. So the bottom line seems to be to test and adjust free T3 levels in order to achieve the Euthyroid state (neither hyper t nor hypo t ) we are all trying to achieve.