Moved to a New City and Became Overly Attached to My Neighbor's Dog

So I recently moved from my hometown to this new city for work. The apartment building is old but charming, and I've really been trying to make friends here because it can feel lonely. One of the first people I met was an older woman named Lily who lives on my floor. Her dog, Max, a golden retriever, practically became my best friend from day one. Every chance I got, I would go down to Lily's apartment and spend time with Max. He loves to run around and play fetch in the courtyard behind our building, and it made me feel less lonely when I was out there alone. The problem is that as days went on, I started feeling way too attached to both Lily and her dog. I'd drop by unannounced just because I wanted some company or a reason to get out of my apartment. Sometimes if she wasn't home, I would even take Max for walks around the block. I know it sounds crazy, but honestly, that little dog became like family. One day, Lily had an unexpected trip and was gone for a week. I missed seeing her every day and playing with Max terribly. Without thinking twice, I ended up taking Max out several times each day while she was away. Then one afternoon when I was walking him back to the building after a long run around the park, someone from another apartment on our floor saw me and asked if I had brought Max here. That's how I found out that Lily had actually given Max dog-sitting instructions with her housekeeper while she was gone. I felt like an idiot. Here I am thinking this dog needs my help and company when really he already has people looking after him. The guilt is eating me up inside, but the good news is that Lily came back today, so maybe everything will be okay now if I just try to keep a healthier distance in the future.