Would you specify which Iodine you can take a half cup of?
Your temp of 97.9 comes at what time of the day? First thing in the morning 97.9 would be normal. 98.6-99.0 is mid afternoon.
Mild Body Odor and phlegm is likely bromine detox. Just be sure you drink salted water throughout the day using unprocessed salt, about 1/2 tsp should help carry the bromine through the kidneys.
I believe Hakala Labs can do the testing you're interested in.