My ha'pennys worth.....
Asthma- as long as is allergic rather than stress induced you should be absolutely fine.
Autism- hang around here and look at us.... there are quite a few people here that I would question where they are on the autistic scale- so probably not a problem.
Swimming / fear of drowning- get yourself a 3mm full body neoprene wetsuit. Do some time in the pool with it. You should discover that it is impossible to sink while wearing it. Then you should be able to start to learn to swim. The idea above of mask and kitchen sink / bath /whatever is a good one too.