Stick with 1913, Paola. If you try spelling it "In nineteen-thirteen I attended..." it works but is a bit clumsy. Linking it to a historical date is even clumsier. "The year before World War I was declared i attended..."
In Australian newspapers the standard practice is to spell numbers up to ten and use numerals after that. Writing good prose is a little more formal, but when numbers get as large as that I'd use numerals -- unless of course we get into super-large number when "3 trillion" would be a fair compromise.