I remember when I first started Lugol's, usually the 3rd day of an increased dose was very emotional and detoxy.
At one point 3 drops for 3 days was pretty awful. Now I can take 20 drops, but even after 3 days I will still feel on the verge of tears or too emotional, or even confrontational.
At least you know that the Lugol's is doing something, and you are experiencing proof that there is someithing in your system that needs to come out!
Maybe try pulsing to give your detox pathways a breather and time to work through some of the crap the Iodine is kicking out.
Good luck!
PS Make sure to take enough minerals and selenium, I noticed a big difference when I started paying attention to that.