I think there are other threads about the issues face by left handed people.
When I am teaching a left handed person, I recommend they hold the pen in the most comfortable position for writing.
I put a small square with a diagonal stroke - which is the 45-degree angle that is often associated with italics.
The person, holding the pen, puts the nib very close to the paper, resting their hand as lightly as possible on the paper.
Then we rotate the paper so that the nib lines up with the 45-degree diagonal on the little square.
This gives the position of the paper and it might be sideways - or even rotated a bit further. Some people end up writing upside down. This sounds very strange, but it actually works out very well.
To learn the basic strokes of italic you want to deconstruct the letters.
Even though I am not left handed, if I hold the pen with my left hand, I can approximate the directions that each stroke needs to follow so a left handed student can see the motions. Mine is not very smooth, but the skeleton is at the right angle and the parts fit together properly.
The biggest advantage to turning your paper 90 degrees and writing from top to bottom is that you do not drag your hand through the ink. So if that is what is working for you - keep going - there are plenty of others who are doing the same thing.
Other tips are to try an oblique holder. I can't describe in words how it works, but for some people it is helpful.
