Hi KMJ,
I've struggled with exactly these issues since childhood - and school days are particularly difficult because of the humiliation involved in coming last in all the races, not being able to participate in competitive sports, etc.
As an adult I ran away from sports altogether and immersed myself in dance and yoga instead, which I loved. That might suit your daughter better, along with martial arts - anything on the scale from tai chi through to aikido, bagua zhang, tae kwando etc.
But re: running and swimming, I finally found some progressive training methods that have allowed me to participate in these activities (albeit at my own pace) - Chi Running and Total Immersion Swimming (you could also look at the Shaw method of swimming - Alexander technique based). All these approaches are non-competitive and work to increase oxygen levels in the body - something we thals need.
Hope this is helpful and let me know how she gets on!