The paragraph has some unclear passages and is not following punctuation and word spacing rules.
I would rewrite it this way to make it clearer and more natural without changing its meaning.
나도 개인적으로 여러가지 일을 하니까 일 때문에 바쁠 수도 있고 일상에서 특별한 일도 없어서 이런저런 소식 전하지 않고 지내게 되네. 연락 없다고 서운해하거나 하지 마. 한국에서는 무소식이 희소식이라는 말도 있으니까 문자에 답장 없더라도 줄줄이 답장 요구하는 글 좀 그만 쓰며 지내다가 좋은 일로 좋은 곳에 가게 되면 사진이나 좋은 소식 전할게.
=> Between being busy with my different jobs and there being nothing special happening around me, I also find myself going a long time without dropping you a line on what's new. But don't feel neglected just because you don't hear from me. I will try to suppress the urge to fire a new message to you whenever there is no reply to my previous one, taking no news as good new like the Korean saying. But I will make sure I update you with new photos and fun stories if I have the good luck of visiting a nice place.