I've been studying English byfrom/via mobile apps.

But I have the impression that these apps aren't pushing me forwardenough to improve my English.

I guess that writing this text, is pushing me forward to improve my English because it is/ it’s a little uncomfortable to me to write this text.

I've been studying English byusing mobile apps.

or "with mobile apps"

But I haveget the impression that these apps aren't pushing me forward to improve my English forward.

"pushing me forward to improve my English" means that they're not motivating you to improve your English. I think you mean that apps aren't improving your English directly. I don't think you mean the apps aren't pushing you. It's subtle but "you" and "you're English" aren't the same. You want your English skill pushed forward, not yourself here (I think).

I guess that writing this text, is pushing me forward to improve my English because it is a little uncomfortable tofor me to write this text.

Same as above - this sentence isn't wrong, but I think you mean that writing this text is helping push your English skill forward, not put yourself forward. You can push yourself to write more often. Doing that writing pushes your English skill forward.

I've been studying English by using mobile apps.

But I have the impression that these apps aren't pushing me forward to improve my English.

Another verb that you could use instead of "pushing" is "motivating"

I guess that writing this text, is pushing me forward to improve my English, because it is a little uncomfortable tofor me to write this text.