It is unlikely that a dead fish would have caused a nitrate spike so soon after death (ammonia or nitrite spike is more likely). High nitrates probably only would have resulted had you left the fish in there to completely decay.
On a side note, nitrates at 10 is nothing to panic about.... but for your SPS I guess it isnt all that great. Softies would like it though
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Did you stir up any sand or move any rock trying to get the puffer out? To me that would be a more likely cause of excess nitrates in the tank. Or maybe the addition of those gobies?
They could have been creeping up on you....
sneaky little nitrates.