>>849 I'm not saying it's impermissible to say that, but there are those who will argue that one cannot feels nostalgic, only nostalgia (because you are not that which you are feeling it about). They are wrong because longstanding practice trumps that sort of theory all the time, but the ambiguity nonetheless creates less aesthetic English and it is a less common phrasing going by Google hits.
That is beside the point, though, which is that 懐かしい is used much, much more freely as a self-expression in Japanese.