Publishers might be reluctant to work with non-native speakers for whatever reason. Sometimes your grammar won’t be an issue as much as your place of origin.
I wish you all the luck in the world with your future endeavours and I hope you succeed at being a full-time writer.
And to get to the point. For me, reading helps significantly. I tend to read every day as long as I possibly manage.
I notice I pick up on style and sentence structure from the authors I’m currently reading. Also, if I’m between books and I don’t read for a few days, I notice my writing changes.