a flow-volume loop (spirometry) will see if there is external compression on the trachea (as would a CT scan). If you have asthma, I am sure you have had spirometry so you could confirm with that doc if the flow-volume loop is negative for compression.
Would also conisder a trial of H2-blockers or proton-pump inhibitors (yes, even if there are no GERD sx) as this can cause these same sx.
The TSH seems high and treatment as well as antibody testing seems appropriate, but my best guess would be that unless there is a large goiter causing compression, the choking/dyspnea is not likely thyroid.
From an experienced speech pathologist's view:
Considering you are SOB and have a feeling of something in your neck, and are experiencing vocal hoarseness, I would recommend you see an ENT and be examined using endoscopy. You might be experiencing some vocal fold dysfunction or have a growth on or around your vocal folds. A good view of your vocal folds might also show evidence of gastroesophageal reflux. Aspiration of refluxed material can occur without you knowing it, especially at night, and can cause the symptoms (SOB, coughing, hoarseness) you described. It can also exacerbate your asthma symptoms. Good luck.
i also have a feeling of something pressing on my windpipe - not constantly - sometimes for hours at a time every day, othertimes short bursts, and othertimes it won't happen for a week.
i have hashimotos thyroiditis.
i know this probably doesnt help much but thought it might help you to know that other people have a similar problem.
i reckon it's got something to do with thyroid, although my docs dont.
there are lots of previous posts on here about breathing difficulties and swollen thyroid glands etc... i suggest having a read through them!
oh yeah and if your tsh is 7.8 you should really get treated!