Well, first off, don't listen to whoever told you that an ESR will tell you you have a viral thyroid infection, that's just crazy, ESR doesn't tell you much of anything specific unless its over 100, and all the things in that range are not good and don't include hyperthyroidism. Sedimentaion rate is really non-specific, they just let your blood sit there and see how long it takes for it to settle. It just generally indicates an inflammatory process.
The only way you can get some really precise information about your thryoid function is with tests. The main test is a TSH and a T4 test, that should be enough to get an idea of what is goin on. You can also get a radionucletide uptake scan that shows you a litter more about function of your thyroid and if you have any increased acitivity in your thyroid gland. You'll get an image that you can actually look at. Treatment option generally include a pill that will radioablate the thyroid. It is hard to give only a dose that will kill off enough thyroid to make you euthyroid, or normal thyroid function. Generally enough ablation is acheived so you are actually a littler hypothyroid. You are not likely to regain any of the thyroid function you loose with the ablation. Once hypothyroid, your doctor will give you hypothyroid medication to acheive a normal thyroid state. This is preferable because the medication for hypothyroidism are much safer and have less side effects then the ones they give for hyperthyroidism. Surgery is generally not helpfull as the thyroid just grows back and you are once again hyperthyroid. The specific symptoms you should monitor are your energy level, are you overactive, gittery or up all the time, generally overstimulated, do you feel hot all the time, this would indicate you're probably hyperthyroid. You may also have myxedema, nonpitting edema that is sometimes yellow or proptosis, where you're eyes bulge out a bit, but these symptoms are usually only present in Graves diseas, a type of hyperthyroidsim. If you are hypothyroid, you will be tired, lethargic, feel cold more often and generally fatigued. This is typical of many pregnant women either during or after pregnancy. You should probably just ask to get a TSH and T4 test done and go from there. It's nearly impossible to tell by physical palpation of the thyroid gland what is going on. You should consider other possibilities as to why you have difficulty swallowing. This could be the result of many other pathologies. Good luck!
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PS here's an interesting tid bid of information, milk maids often had goiters or enlarged thyroids in the dark ages due to iodine deficiency and its actually still seen or considered atractive in some areas of the world such as parts of India where some people consider it a sign of fertility!