Yea, it does sound like the poor shark was going to die soon.
On it's back & breathing fast, are generally very bad signs.
But still - as a generally rule a Nurse Shark is a bad choice for a pet shark in your home aquarium.
Although they usually are very hardy sharks. They get very large - mature at about 7-8ft, and usually reach about 9-10ft in captivity. Also for a bottom-dwelling species they are fairly active(every notice nurses swimming around at a public aquarium).
The fact is to keep a nurse shark for it's entire life - you'll need a large shark pool(at least 6,000 gallons).
And because Nurse sharks are so cheap(if one can call a $300 fish cheap)- - it makes it the 2nd worst shark available for home aquariums, & to shark hobbists(actually Lemon sharks are worse - because they are require a much larger pool & have been known to attack people, - unprevoked).
I would have added Bull Sharks to the list - but Bull Sharks run about $6,000-8,000
a piece. So these are general out of the price range to most shark hobbists. Also most dealers that sale Bull Sharks, will only do so to very experienced profressional keepers or large public aquariums
Just, don't buy a nurse unless you have a huge shark pool !!!