As soon as she made Nathan fall in love with her, first of all she tried to get rid of his friends. I mean, she didn't approve of us meeting, and set his mind against me

Very good! Just a few things:
◉ ...fall in love with her, THE FIRST THING SHE DID WAS to get...
◉...rid of ALL his friends
◉ BY THAT I MEAN [no comma] she didn't...
◉... approve of us meeting UP
◉... and TURNED HIM against me
Make these corrections and add it! 👍🏼

Thanks Uly, that would be too many fixes to call the translation mine )))
Can you explain why you don't like "I mean"? That seems a standard start of a sentence in verbal talk.

When someone asks you what you mean, then starting a sentence wit I MEAN sounds natural:
Uly: Nick, let’s go to the movies. Anna wants to go too.
Nice: Nah, you guys go ahead. I’ll wait until the company is more conducive to watching movies.
Uly: What??? What do you mean?
Nick: I mean I’ll wait till it’s just you and me. Anna insists on sitting right next to me and munching popcorn throughout the whole movie and it drives me nuts. I’ll take a raincheck.

However, when you state something and then want to expound on it, it’s more natural to use a phrase like WHAT I MEAN IS... or BY THAT I MEAN... (as in this example).

So I guess what I didn’t like about it, is that it didn’t flow.

Don’t mind about the fixes - this is meant to be an exercise and writing correct sentences out is good for your brain 👍🏼😉

That's why I keep doing it - exercising my brain )))
Thanks for your detailed answer!

You got it!