Should I '20M' fight for the woman I love '18F'?

Hey I'm '20M' I've always been kind of a weirdo and I'm not great with women so I'm not used too girls being friendly with me. I used too work at this gas station/ restaurant and I had friends there but one day I met this girl (Leats call her Sam '18F' ). We've been very friendly towards one another and one day while I'm cleaning Sam and her sister is about too leave and while I'm not realizing I bumped into her she put something in my pocket and I didn't know what it was and a little bit later I checked too see what it was, it was her phone number I called my best friend (let's call him Tyler '18M' ) I asked him bro what does this mean he said "Bro, she likes you just be nice and respectful. And the rest will come naturally. " (he's very spiritual). I texted the number and it was her and we've been texting for awhile now at least but then it was everyday and she confessed she had feelings for me. I was in shock and didn't know how too take it keep in mnd this never happens too guys like me, but the problem is that it's a little age difference I'm and I didn't think it would look good I was scared of what people would think so I rejected her over it, I was upset because I also like her but I didn't know how people would react. Well later on we stopped talking for a minute but at the time I blame myself I was doing some down right dumb shit trying too be someone I'm not, it took me a minute but I found myself. And now I'm doing better I'm not at that same dead in job, I'm working at a factory and I love my job, also me and Sam started talking again and my feelings burn brighter and after talking with alot of friends and family I decided too say fuck it and asked her out too get Mexican food (she loves Mexican food and I can't stand it) but when I'm with her and we eat everything's just better the food, water, air, hell everything truly. I know I'm being much but I just can't express how much I love this girl I've met her parents and she's meet mine, but I asked her what we are she said she doesn't want too date me but we are still planning these dates and we call each other like bby, my love, sweetheart, ect. But I will say I know she's still hurt from my biggest mistake saying no first if she really doesn't like me she would've said no when I asked but she said yes and she has done something not many people do for me she knows I collect and loves it and on our first date I bought her some cheap earrings but she really loved them so we walked into Ross at our local mall and saw this cool Marvel figure I pick it up thinking about buying but I didn't want too nerd out on my first date but she saw my put it down she asked "Why did you put it back?" I, replied "I don't want too seem like a weirdo in front of you." She thens proceeded too pick it up and buy it for me and she said she loves weirdos and I hugged her and asked too sign it because that's my most prized thing I own and too know something about me I give gifts too loved one too show my love not everyone does it back and I don't get upset about it but when someone does that for me it means the world, Tyler did it my other buddy Zack '24M' as well. But when she did that for me that's when I knew I need this women in my life someone who likes and cares for and about me and doesn't want me too change. I really feel like I'm falling in love with this girl, and I know at the moment she doesn't what too say we're dating but we are, we going on all these dates and how much we care for one another I believe we are I just think she is still heartbroken over me rejecting her the first time but I want too fight for her I want too show her I really do love and care for her. Should I keep fighting or give up? Me personally I want too fight for the women I love but I need help on this because I need too know that I'm doing the right thing.