I assume you are using bromine tabs and shocking with either MPS or chlorine and you added sodium bromide on fill to create the bromide reserve in the water.
What is your pH and TA. Bromne tabs are acidic and can cause pH and TA to drop (much like trichlor tabs do in swimming pools).
This is a problem because at low pH elemental bromine can form in the tub and outgas. Elemental bromine is toxic (similar to chlorine gas, which it is related to). If your pH and/or TA is low then bring it up and keep it up. This should solve the problem. A properly maintained bromine spa has a slight 'chemical' odor a bit more noticable than the odor from a properly maintained chlorine spa. Bromamines have a 'fishy' odor which can be lessened by shocking the spa and leaving it uncovered with jets and blower (if so equipped) for the more noxious oxidation byproducts to gas off.
coughing in the spa is often from either elemental bromine (dangerous!) or oxidation byproducts from not shocking or improper shocking.
Finally, do you have an ozonator on the spa? Ozone itself is toxic and can irritate also. There should not be an ozone residual in the water but that is not the case most of the time (to save money on the ozone system, unfortunately!) Once again, leaving the spa uncovered and running the jets and blower for a5 minutes or so before entering the spa can help. Better yet, turn off the ozone, if you can, before aerating and while using the spa. Depending on your model spa and ozonator this may not be possible.
Hope this is helpful.