Don't use either Bromine or Chlorine. Both will interrupt Iodine utilization.
Look into GG's suggestions or I just talked to a couple of people last week who both switched over to a salt based system and they love it. Sounds like it is an investment $1000-1500 but it is your health!!! And if you have read anything here about Iodine you have learned that the whole point is to get Iodine (good) in you and get the other halides (bad) out of you. Of course acknowledging that NaCl Chloride is good for you.
And if you have Fluoride in your water supply and don't have a water distiller an RO unit you should really look into getting something to get the fluoride out of the drinking water.
And a shower filter or whole house filter to get the chlorine out for bathing is a great idea too.