You didn't indicate what the shortened vs the passport names were, but I sincerely doubt that you would be barred from traveling. If you have a birth certificate or any other documentation with either version of your name, take it with you. You might get questioned a little but I doubt anything other than that.

Also, I suggest you call the airline directly and explain the situation. Give them the name on the passport and also the passport number. They will put a note in your reservation that should minimize the problem at the airport.