Seeking advice about my first time dating
So I met this girl online 3 years ago and we started chatting. At first she seems quite keen on chatting with me and we don't talk all day and night, but maybe once or twice a week, but the conversation were mostly sharing brief information about each other and pleasant compliments. During this time, the girl did mention to me things like gemini and libra are a good match and kinda let me know she enjoys our little chats.
After a year she said let's go on a trip and we did, she planned the itinerary and booked the hotels. I went to her country but it's a different city cause she wanted to go on a trip to another city. So I went there and she was reliable, friendly and really kind. She tried to accommodate me and brought me to try the foods I wanted even if it's not her preference. During that trip I was a little sick, and the cold weather was also affecting my desire to go out much and I felt quite tired at the end of the day. I was surprised she only booked one room with two beds, and I didn't know she trusted me enough despite our first meeting. But I didn't take the opportunity and I barely talked much with her in the room, and honestly I felt her looks was not really like the pictures. There is definitely photoshop done but she's like 80% similar to how her photos are. So that was the first meeting and I probably was not proactive enough. I also realized she wanted to split the bill on everything and didn't expect me to pay.
After a couple months, I had a business trip to her country and I took the chance to meet her. She agreed to meet me after her morning shift on a Saturday she took me around her city and treated me to coffee and lunch and dinner. She even invited her brother to have a meal together with us. She told me it's her treat since I visited her city. I looked at her in a different light this time and I realized I missed out and I messed up.
After the trip we continued to chat and things were kinda back to the way it was, just occasional pleasantries and brief update about each other. And one day she mentioned about coming to a city in my country for a trip as her friend went there before. So I gladly agreed and welcomed her. So we arrange for the trip and she did the planning again as she normally prefers to do these things. So when she came, I welcomed her and we enjoyed the trip and this time she booked an apartment with two rooms. And overall it was pleasant and I decided this time I will be proactive to let her know I'm interested. But at one moment while taking her picture, I noticed she had underarm hair and that threw me off a little... I know it's immature of me but it's the first time I'm dating a girl and that I've seen these kind of things. So I held back and didn't really let her know my desire to be clear about our relationship. And I feel I messed up again. I also realized it was not easy for a girl who went on a trip and had her period on the last day and had to take a flight home.
As we went back we did continue to chat as usual but I realized we never called, just strictly chatted the whole 2 years. And now on the 3rd year I invited her again to come to another city for a trip. And I was sure I would be forthright about myself to her. When discussing about the upcoming trip, I mentioned briefly to her that we're both single, we could consider to be a couple, I mean why not? And she thought I was joking and she aske dif my parent allowed me to marry a girl from another country. I said they would be happy if I can find a girl I loved and marry her. And I said let's talk about this in person. Soon the time for the trip came, and this time I did the planning and booked the hotels. But despite me booking the same one room two beds setup, this time she said she preferred her own room as she needs to have some time on her own to unwind. I did feel rejected but I let her do as she wished. During the third trip I definitely let her feel I cared about her and was more proactive. And during the last day, her period came again. But this time I was prepared with ginger tea and she appreciated it. On the flight home, I told her we've known each other for 3 years and I've found her more and more attractive and I'd like us to consider being a couple. She agreed we're quite similar and can match well with each other. But she said she want to consider factors like family approval, LDR and future relocation factors. I agreed and told her let's think about it together. In the end I told her I appreciated her take time off from work to come meet me and that she enjoyed the trip. So I didn't ask her to pay me for it.
When she returned back to her country we did chat a little bit more frequent now and I thought it was a hint I need to be more proactive. One day when she posted on social media that she's frustrated and unhappy. I tried to let her know I would be her listener and I am serious about being with her. She left me on read for 5 days and just said she had a tiring week. And she went to hike the next day and she just gave me brief updates like her departure so I wished her safe trip and enjoy herself. And after a couple of days I send her a message and she briefly mentioned she talk to her mom about me. I was surprised and I told her I'm grateful she did that and she can tell me about it when she has time. But she never did. And ever since then I felt like I have been rejected multiple times and didn't look for her. But occasionally she'd send me her gym picture updates and her cute pet cat who she refers as her baby. I just replied to them with a statement because I didn't want to ask her any questions.
So fast forward a couple weeks I had a long weekend and I asked her if she want to go on a date with me. And I could find a affordable flight to meet her. But she said she had already planed a hiking trip with her friend and it wasn't easy to find a group to go together and share the cost so she could not change the schedule. She also told me it's too far. So I just told her it's fine, and I understand and just switched the topic about a coffee recipe I'm trying lately. She responded with enthusiasm as she love coffee and the conversation ended.
From these interactions, I wanted to know if I should still try? Or should I just give up on this girl? Sorry for the long post, I just wanted to give as much context as I can.
TLDR:
Trying to know if the girl is worth getting into a LDR with. People form 2 different countries. She trust me enough to travel with me to a different country she doesn't ask me to pay or expect me to spend on her unless I'm willing to do so. But when I decide to express my desire to be with her, my messages don't get a reply for days. And when I offered to meet in her country she doesn't prioritize me. That's basically what I feel, like she doesn't really prioritize me. Also she's 32 and I'm 29. All opinions are appreciated from men or women. Thank you!