While it is estimated that there is only about 1 fatality for every 200,000 dives, about half of these occur in divers with fewer than 20 dives under their belts.
There is nothing inherently safer about a "shallow" dive. A ten-metre (33 feet) dive can be just as dangerous as a twenty metre (65 feet) one. Unlike football, you can't take time out on the bench if your exercise capacity lets you down. If you have a panic attack or a fight with your mask you will be breathing water, not air. Not everyone is medically suited to diving and when things go wrong underwater, they can really go wrong.
A Dive Medical is quite extensive and should be done by an accredited doctor and involve a lung function test. There is considerable controversy about whether asthmatics should dive at all. If you really want to learn to dive and have asthma, or any other medical condition that could preclude diving, allow plenty of time before your trip to get your medical done at home.