I said, I don't remember where, this sentence: Я счастливый. And somebody corrected me to say: Я счастливен.
They could be right in that your phrase was not entirely correct -- depends on context -- but there is no such word as "счастливен". What they most probably meant was "Я счастлив".

Счастливый and счастлив are adjectives, full and short form, respectively.
You may want to read another thread on this topic: Краткая форма прилагательного

They said to me -ен is for men and -на for women. Is that correct?
It is partially correct. It does not apply to all short adjectives. Only to some.