When I was younger I once choked on some food and started coughing heavily, my Dad then told me to raise my arm in the air in order to "help raise the diaphragm". It actually helped with the coughing and helped me breath better. Since then I'm used to doing it. Does that really help, are there any medical proof or is it a urban legend ?
With arms raised oxygen uptake is increased for normal breathing, see Couser JI, Martinez FJ & Celli BR (1992):
The increases in [oxygen uptake], [carbon dioxide production], [minute ventilation], and [tidal volume] during arm elevation persisted. for 2 min after arm lowering (...) We conclude that simple arm elevation during tidal breathing results in significant increases in metabolic and ventilatory requirements.
Unless the esophagus is fully blocked Raising the arms will therefore increase oxygen uptake in healthy people, which may make you feel like you are not choking anymore.
Note though that raising the arms is not an appropriate method to help a person who is actually choking. Unless the person is able to breathe adequately the Heimlich maneuver should be performed if coughing does not solve the problem.
[warning, anecdotal] My tennis trainer always told us to put our arms up and breathe in when panting after a demanding exercise. During Yoga and other 'breathing exercises' the arms are usually also repositioned to either limit or maximize lung volume.