Yes, your response “this has been me since my sister traveled” is grammatically correct. It means that you have also experienced living alone and perhaps feeling indifferent about meal choices or not prioritizing cooking for someone else since your sister left.
You could rephrase it in a few different ways, such as:
- "I can relate; I've been like this since my sister went away."
- "That's how I feel too, especially since my sister moved