I want to keep trying because I'm willing to bet many guys who liked her gave up quickly. But if there's no chemistry, I feel like I'm being a shallow bastard paying so much attention to a girl who I don't actually enjoy being around.
Can anybody offer thoughts?
If you don't feel like there's chemistry and she's not showing any particular interest, then go elsewhere.
She will find someone who she can open up to and you will find someone who suits your needs as well.