My impression is you are not being natural. You do have pitch issues, but to me is you are not relaxing your voice and that is causing your pitch issue. Try again but me more natural, find the range that works for you, then work on the pitch.
I always found using something like Waves tune, it is not very expensive, use it to tune the vocal track, look to where you are off pitch and try to correct it with a new recording until you you know the correct pitch.
That recording seems you have no feel for pitch. I would work on that with something like Waves tune and keep tracking the vocals until your vocal pitch is closer to the target pitch.