In the end, LondonJ did exactly the right thing. Faced with symptoms of a potentially very serious condition, he diverted and got medical attention for his passenger. An aircraft is not the place for untrained people to be making a complicated diagnosis and providing treatment on the basis of that diagnosis.
Yes, breathing into a bag can relieve the symptoms of hyperventilation - if that is the problem. It could also significantly reduce the oxygen supply to a damaged or dying heart or brain. Unless you are very sure (and I'm not sure how you can be in the circumstances), the safe thing to do is to seek rapid, qualified advice.
Cheers,
BM