It looks like somebody tried to "honor their Irish heritage" by inventing this awful faux Celtic mess and giving it to their poor daughter. Sheila is a nice name, Sheelagh is a sneeze.
Its a unique spelling, I'll give it that. But when I first say it I honestly could not believe it was pronounced as "Sheila". But if its your name and you like it ignore what I'm saying! Personally I think Sheila sounds very nice out loud.
I can believe that this collection of letters has been used maybe once or twice, sadly, but I don't know if that alone is enough for its inclusion in the name database.