You should have no issue taking your nasal spray with you in your carry on I don't think. I would check with the airline before heading out though. If not, take your script with you.
Many will take some energy shots in their carry on bag too, just in case.
As urs said, hyperventilating can be a big help in slowing or stopping a hit at times. I would not use the bag though, as you want more O2 not the CO2 you exhaled. Just breath in deep and exhale with force. Repeat. It helps clear the CO2 out. If others are around, then do a long exhale instead of faster and with force. But inhale quickly and hold it for a few seconds.
As for the Pred - I would start it the day before my flight. Then have a new taper pack for the return trip. Assuming that you will be there over a week of course. You normally would not want to take to taper packs back to back. But this might be a special case scenario. Not like you are going to be taking the stuff daily for your entire cycle.
Sorry, that is all that I can think of at the moment.