No, you can't be both. That you both extravert (with intuition) and introvert (with feeling) doesn't mean you have two psychological types. No, you can't be both. Your type is one or the other, or something else completely. No, you can't be both.
"There can be no understanding between the hands and the head unless the heart acts as mediator." (Metropolis, 1927)
I do feel like I am an ENFP, but I do operate and make decisions as an INFP a good part of the time. I am VERY sensitive, and even though I am working on it, I will get my feelings hurt and revert to INFP. I am aware of it now, but before I couldn't explain what was happening before.
I also see I have been almost exclusively acting in INTJ shadow mode for years due to stress. Not just in situations, like with INFP, but for huge blocks of time. I was a different person and I was pretty miserable.
I see I have been very introverted for most of my marriage, and a good chunk of my childhood/teen years. I feel like I did it out of survival, but I am much happier and natural when I am able to extrovert and "feel like myself".
So yeah, I am pretty much the typical ENFP who has all kinds of reasons for why I don't act typical