Hi there!! First of all, just wanna say that i'm also in uni and i'm very introverted with few real close friendship experiencies, so i hope i can be of some help or at least comfort.
I can tell you value that friendship a lot as it's also lasted a couple of years.
But in your case I would mostly prioritize your exam this following week as i imagine it's a huge step. (Btw i hope everything turns out great with your exam and the PhD (โงโโฆ))
I'd try to keep on contact with her and be the "bigger person" and send a message like ' i'm sorry i can't hangout with you right now. I really wish i could, but I'm really stressed with this exam. But once i'm finished with this one, we can meet at your place or mine and celebrate if everything turns out well '. Hoping that with that she stops giving you the cold shoulder.
Having said that, it's giving me weird vibes a couple of things from her. Like her wanting to meet only in her place and all those excuses are suspicious. And second, her attitude is really weird, i don't know if she got mad or something but from a 3rd person view, one should be understanding that you have this big exam coming up soon and would ask first if you have time or energy to meet up or should offer to be the one to travel this time. Also you didn't say that you couldn't hangout, just that you couldn't be the one to travel 3 hours... I don' t mean to offend your friend because they are surely good people but i really feel for your situation.
I think there are many things bubbling underneath that you guys need to talk about face to face. As you've said in that paragraph of you feeling like she may think that you've got a lot if free time and so, which is not the case.
I've heard that once you graduate it can be challenging to keep meeting up with your friends. So it's not that uncommon, but i'm sure that if talk things out, it will make things smoother next.
I'm sending you much love and strenght and hope i wasn't rambling nonsense. I hope you can patch things out with your friend. And i'm sorry for any mistakes, english is not my 1st language)

I don't have friends to rant ab this so I'm just gonna drop it here on the forum.
I have a friend I met in Uni. We have both graduated and we live towns apart(approx 3hours). Thing is I am preparing for PhD while she's working as a teacher already. Thing is since I've been preparing for the exams (we have entrance exams for PhD) , I've gone recluse for over an year. It's not like I don't meet people, I do but over the year I've grown from being an extrovert to an introvert(I've found the joy of being a homebody, also greatly broke). I've visited her like 3 times and stayed over for weekends at her house. She has met me like once when she came to my town. The thing is she knows I have an exam in a week and she asked me if I'd visit her and stay over. Now usually I'd just say okay and make a plan but rn I'm not in a position to be anywhere except my home. I told her it isn't possible because of unforeseeable circumstances and she was pretty bummed.
But the thing is over the past 1.5years, I've asked her multiple times to come over to my house and stay over. Even asked her if she would want to go for a weekend trip but she told me she was short on money and when I told her I'd cover, she made some other excuse like being on her periods at that period of time.
I don't know if she thinks I'm always available just cause I'm unemployed but I have chores and I need to study. Plus I am super broke and can't even afford to travel right now.
Now she isn't speaking to me and if I text her she gives me dry replies. I know she's a very sweet person but idk what to do.
Anyway that's the rant