My only concern would be the concentration. After Molly's experience with straight Lugols in her ears, the lung tissue is at least as delicate and even more critical. You need enough to kill parasites but not so much that you get abcesses and then have serious trouble breathing.
Do you have any idea what the parasites might be? Years ago (like 15 or so) when I took classes from hanna Kroeger, she said that Ascaris cause asthma. But I am not aware of them migrating up to the sinuses. However, you may have such a large population that they dop. Anyway, she has herbal formulas to take care of different types of parasites. Unfortunately I don't remember what most of the formulas are. however, Kroeger Herbs may have their formulas on the web these days. If not, the retail store (Hanna's Herb Shop in Boulder, CO) could send you a list of their products. I would be inclined to treat with a parasite herbal formula for a few days to weaken them, then continue with the herbal formula but introduce the Lugols to go for the jugular. Otherwise, they may just migrate out of the lungs to somewhere else. But if you are treating with herbs systemically, there is no where to go. I have used Hulda Clark e's method (back before she made her own products and used Hanna's Wormwood combination). She recommended taking 2 caps the first day, 3 the second day, 4 the third day, and so forth till you built up to about 10 caps taken all at once. Then taper off 1 cap each day back down to nothing. I would stay at the 10 caps all at once for about 3 days to ensure I had killed them. By going up to the high dose, Hulda Clark e says the herbs get in the blood stream and that that combination of herbs would kill over 100 varieties of parasites, and kill them in the blood and organs. The formula does not kill tape worm, but pretty much everything else. The bottle meets FDA guidelines in that it just says take 2 caps. But at that amount it only stays in the intestinal tract. You don't want to keep the extreme high dose for too many days as one of the herbs, so I have been told, can become hepatotoxic if taken in high doses for too long. How long is too long? I don't know. So I just did the 10 caps for 3-4 days and then started lowering .