You might need to dilute the Lugol's a little more. It could cause gastrointestinal discomfort, just as too much hydrogen peroxide would.
Aloe vera juice would help your indigestion if it's not related to the iodine dose. A few ounces before each meal should work. And try a more dilute concentration of Lugol's. I can't even swallow 4 drops unless it is in at least 9 ounces of water.