Both are correct, though the first sentence definitely is more common (or "the first sentence is definitely more common" either way is fine). The latter is perhaps more formal, and more suited for written language than it is for use in conversation.
In some cases there might be a different connotation, though:
I was suddenly feeling quite sick
I suddenly was feeling quite sick
I was feeling quite sick, all of a sudden (not really relevant here)
The first example stresses the sudden onset of sickness, whereas the second example puts the adverb first, to emphasize that it all happened quite, well, suddenly.
The third example stresses the feeling even more, and adds the fact that it happened suddenly in a sort of "in retrospect" kind of way.