Me [25 M] with my former [25 F] 3 months, long distance; it was short but I'm struggling to get over it

I've lurked around this sub a lot, found great advice and comforting words from this community,

I met this girl at the very end of this masters program in Texas we were both in. We had had dinner with mutual friends 2 weeks before I left for Nevada in October, and had our first date 5 days before I actually left. She was headed to Virginia. So we both knew it was probably a bad idea to start dating long distance, but I had been in distance before and knew how to handle it, so we both figured why not. To make the distance bearable I scheduled Pho dates via Skype, asked her to teach me to make her favorite dish via Skype, sent her her fav flowers, things of that nature.

After our first date, I stayed at her place the next 5 days, then left for Nevada. We talked everyday, whether it was calling or texting or FaceTime. Flew to Texas to see her for thanksgiving, then flew down again for New Years. Everything thing seemed fine after I got back in January, but 2 weeks after I got back she took longer to respond to texts. I brought up my role in her life (as the guy she's dating) and she said we needed to talk.

She ended things right there, kind of surprising me. She is very independent, has lived on her own the last 3-4 years. Prefers to live by herself.

Her main reasons for ending it are valid, and I agreed with them: Distance, timing, how fast the relationship developed. But also expressed how I couldn't talk to her the way she talked (if that makes sense; she uses a lot of slang). She also pointed out how she felt teaching me how to cook different types of meals was a burden on her because to her it seemed like she was teaching me to be mature. I have cooked for myself throughout college but kept it to chicken, some fish, veggies, eggs, etc.

I emailed her letting her know I still cared for her and wanted to keep her in my life as a friend because of how much she contributed to my growth as a person. I did mention I still felt there was a spark there and wanted to maybe come back to this down the line.

Well I found out the day before Valentines Day she was seeing someone else. She also texted me wanting me to send back all my stuff. I get that and am thankful, but it hurts. I felt like our time together didn't mean anything to her, as short as it may have been.

I'm trying to understand why I still have a hard time getting over her even though I physically spent a total of 15 days with her. I understand 3 months is hardly anytime, but the physical chemistry between us was the strongest I've felt. Physical chemistry isn't enough to maintain a relationship, distance at that, but I felt we had a close enough emotional connection.

I guess I'm looking more for understanding here. I want to reach out and maintain a connection with her, but I get the feeling she doesn't want anything to do with me. I try to be on good terms with my ex's because I think each of them has made me a better man in some small way. Is there no point in trying if she isn't willing?

Lot of context is left out, would make this post way too long.

tl;dr: Dated long distance for 3 months; she ended out of the blue; I fell very hard and am trying to move on. I want to maintain a connection but she doesn't sound interested.