You are brand new to treatment, and it's too soon to say you aren't taking enough hormone yet. Thyroid hormone dosage has to be started low and increased slowly over a period of months before you will reach your optimum dose. Increases are made at 6 week intervals. Trying to go faster than that can cause an adrenal crash, and that ain't fun.
There are a two common things that often happen after you being taking thyroid hormone that MDs don't tell you, because they don't usually know unless they are hypothyroid, too. Your symptoms can worsen and/or new ones can appear. I'm pretty sure that's what's happening to you now, but it will get better with proper treatment.
When I was still untreated, I had the frequent sensation of a golf ball stuck in my throat. I also had a maddening, intense itching deep in my throat which I once tried scratching away but succeeded only in scratching my skin raw. Both sensations were definitely from thyroid inflammation due to antibody attacks, and both went away once I found my optimum dose.
Try to be a patient patient, and be prepared for weird things to happen before you find your best dose.