Many people claim they catch colds (etc) when travelling - but the aircraft cabin isn't the place they catch bugs. Travelling involves standing in numerous queues with the unwashed masses, and local transportation often in 'public' conveyances without any filtering (think about a taxi).
This is what
Boeing has to say about air filtering on their aircraft. Note that the B737's first flight was in 1967 - unlikely you'd find one that old but systems will differ on the age of the aircraft. The B767 is newer - first commercial flight 1982.
You can avoid some of the queues, she doesn't have to stand with you while you check-in / drop bag or at the gate (wait until everyone else is on) but with security it's pretty well mandatory (although you could ask for assistance - and have your partner escorted through). Wash hands frequently too. Also use disposable masks (found at any pharmacy) but be careful - they lose their usefulness once touched, so she could need a few.