I'm afraid it is not correct.
"with" is translated as "-(으)로" if it expresses a means of doing something.
For example, "Drove the nail in with a hammer" => 망치로 못을 박았다.
"With my program" in your example doesn't indicate a means, though. It instead sets the topic of the sentence, like "as for my program" or "speaking of my program", etc.
Such phrases of setting the high level topic are best translate using the 은/는 topic particle.
So, the sentence can be translated as 제 사진 프로그램은 dpi 를 바꾸면 사이즈도 비꿀 수밖에 없어요. (dpi may be translated as 해상도 = resolution).
- In my family [As for my family, Speaking of my family], everyone is healthy => 우리 가족은 다들 건강해요.