The Unintended Roleplay

I'm a personal trainer at a gym here in the city. I've always been called 'Daddy' by some of my clients as an endearing term, and I never really thought anything about it until this past week. I was working with a client named Sarah, she's in her mid-twenties, just started the program a couple months ago. Sarah had come into the gym looking stressed out and asked if we could start a bit early; I agreed. During our session, she kept making comments about how I'm like a father figure to her and was unusually clingy, hugging me before leaving and asking when we could have another appointment next week. At first, it felt odd but not entirely unwelcome, as the connection with my clients is important in this job. Afterwards, she messaged me about getting together outside of training for a meal or something casual, which isn't normal behavior from any client. I tried to politely decline and suggested we keep our relationship professional for her sake. But then she texted again saying that she needed someone to talk to and seemed to take it personally that I wouldn't meet up. Feeling guilty, I decided to let it slip when she was at the gym next time, so we agreed on having coffee but kept things light until she brought up 'Daddy' again. She asked if I'd ever thought about us being more than trainer and client. It hit me then that there's been an unspoken attraction between us from the beginning, but it had never crossed my mind in a romantic or sexual way. I explained to her clearly that while she was sweet and doing well in her training, this wasn't what I signed up for as a professional trainer. She got upset when I said no again but left the gym with some hesitation in her eyes; we didn't speak much after that except for work-related things. I hope I did the right thing by keeping it strictly business because now I feel conflicted every time she comes into my training sessions.