A feeling of fullness is common, regardless of the medication you're on. It's possible that your thyroid is swollen or there's a nodule causing issues; however, anxiety can cause the same feeling, even when we don't particularly feel anxious. I had the choking feeling for a long time; a swollen thyroid was partially responsible, but it was caused mostly by anxiety.
Wouldn't hurt to ask for a thyroid ultra sound, just to be sure.
I am taking Armour Thyroid and do not have the issue with my throat, post results as goolarra has advised and also, an exray would not detect an enlarged thyroid, which could cause throat or issues swallowing, your MD would more than likely send you for an ultrasound. This would show any issues and is common with thyroid. Mine came out 2.5 times the size of normal on the right side, I did have issues breathing when sleeping at that time. Best Regards FTB4
Often just being "in range" isn't good enough. We all have our own personal range, and many of us do not feel well low in the ranges.
Please post your last labs with reference ranges as they vary lab to lab and have to come from your own lab report.