Hello madiieienf,
After reviewing your post, it sounds like you want photos from the iPhone to get to the computer. You don't want the existing computer photos to be added to the iPhone. I would recommend that you read this article, it may be able to help the issue.
This explains how to get the photos to the Mac, and explains what would have to happen to get new photos onto the iPhone.
My Photo Stream FAQ - Apple Support
With My Photo Stream, you can access the recent photos that you take with your iPhone, iPad, or iPod touch, on your Mac and PC.
Photos that you take on your iPhone, iPad, or iPod touch will automatically upload to My Photo Stream when you leave the Camera app and connect to Wi-Fi. And new photos that you import on your Mac to iPhoto or Aperture automatically upload when you connect to Wi-Fi or Ethernet. You can change your iPhoto or Aperture preferences so that only photos you manually add to My Photo Stream upload.
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Have a nice day