Here are two famous acupressure points that are very useful for self-help.
Hegu is well known as the headache point. Find a sore spot in the meat of the hand, between the thumb and first finger.
Hegu is also useful for colds, sore eyes, toothache, and allergies.
Neiguan is the famous motion sickness point.
It is located about three finger widths from the wrist, between the two tendons on the palm side of the arm.
Neiguan is good for all kinds of nausea including morning sickness, tightness in the chest, tight diaphragm, hiccups, and insomnia.
When you have one of the symptoms hold or massage the point for a minute or two, or until the symptom goes away. On a very bumpy flight I hold neiguan until it gets smooth again. It is also a good point for calming anxiety.
If someone faints, try pressing quite hard between the upper lip and the nose. Of course, always seek medical attention when appropriate.