Throat feels swollen and hard to swallow? thyroid?

Less likely: More likely a throat infection, and less your thyroid. If it gets better and you do not see or feel a bulge in your neck/thyroid, it was probably an infection. If it persisits, you could always be checked by a dr. And a simple thyroid test would let you know.

Probably not: Your thyroid would have to get really large before causing swallowing problems and it would come on over a fairly long time.

Sore throat: Throat swelling and soreness can be due to an a virus (cold) or bacterial (strep) infection, post nasal drip from nose congestion, heartburn, smoking, air pollution, or even yelling. It is much less common for an enlarged thyroid to cause a swollen throat but if you have a thyroid problem, you should have your doctor exam you. Fortunately most sore throats are minor and go away by themselves.