Should I cut this off or continue pursuing?

Firstly, I’m a guy, but my account says female for some reason.

I’ve been seeing this girl for a few months, and I’m unsure if we’re compatible long-term due to our cultural and racial differences (she’s South Asian, and I’m Caucasian). I find her attractive sometimes, and she’s generally open to hanging out but refuses casual sex. She does things that make me feel certain emotions, though it’s not love. A few days ago, I walked into her apartment (which she’s okay with) and heard her humming in the shower—it felt very innocent. She never turns down spending time with me and even planned a beach picnic when I suggested we stay in and watch TV. We mostly hang out at home; I don’t take her out on dates or spend money on her. Still, she giggles and playfully tickles me when we’re together, and I enjoy those moments. I don’t want a relationship with her, but I find myself wanting to see her every two to three weeks, even though she won’t have sex with me. I’m not sure if I’m leading her on or if she’s playing me. She doesn’t ask for anything, sometimes falls asleep in my arms while we watch TV, and I’m unsure how to handle these unfamiliar feelings. I don’t think I’m falling for her, as I’d want to see her more if that were the case. Can anyone relate? Should I end this, and what should I do if I get bored and want to spend time with her?
Should I cut this off or continue pursuing?
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