Most of us on T3 med, myself included, find that by splitting our dosage into 2 doses - I take one in the morning and one about noon - it keeps our FT3 level throughout the day, so we don't get the peaks and valleys of having way too much, then way to little, which in itself, could cause the anxiety.
Another thing you might want to consider is a different
brand of Levothyroxine
. There may be fillers/binders in the synthroid, that are causing adverse reaction, which manifests in anxiety.