yes some type of immune reaction perhaps, wouldn't say its part of detoxification though. this is a common term missused by naturopath folks, when in actuality its called a side effect/reaction, as u build tolerance to drugs sides often diminish... it could be additives/preservatives used that are causing the reaction. you could try oral GT and see if it persists.
could also be some sort of downstream effects knocking things out of balance and causing the sinus issue.NAC for example has effects on mucus membranes so perhaps along similar lines and the thinning of the membranes may cause irritation/swelling? just a thought. may also have effect on BP causing "pressure headache" type symptoms, elevated and dropping BP is known side of glutathione...
on a side note I find it paradoxical that they say low GT levels increase risks of infection however thinning of mucus(via NAC to increase GT) also allows infections to garner access to cells. IMO its always a balance and everything has pros and cons, no matter how benign u may think they are or how "Awesome" they are for u. for example antioxidants have been discussed as potentially increasing risks of cancer as we need a certain amount of oxidation to kill off "bad" cells. everything is fortified with iron however now we are learning that for most folks who dont need iron it gives more oxidative stress. similarly mega dosing of vitamin C causes high uptake of said oxidative iron..
WE will see a shift in supplements in the future as cheaper easier testing is available and this idea of mega dosing every vitamin for every person will fall out of fashion esp as more information comes out about how some vitamins may actually be causing you to be deficient in others unknowingly. there is alot we don't know even about vitamins and minerals and many of the working theories are often contested.. lol all that is to say, not all that glitters is glutathione and neon pee may not be the path to health...moderation/balance in everything..