E3 would be the right era serial number for a May 63 Sting Ray, and the only frame used from 63 to mid 65(?) are short frames - The later "Junior" model is the same frame; they just called them juniors after the longer frame was introduced after mid 65...
To verify it was a originally built as a Sting Ray, you would have to see if the original red matches the terra cotta red. I think the other Schwinn models had the more commonly seen radiant red. I've never seen a Terra-Cotta bike in person, so I couldn't judge which it is. Cool find regardless - I'm jealous!