I (23M) am handeling my GF's (20F) sad moods poorly and it could be disaterous

Hello reddit,
first time posting here so I might forget some details, let me know if I there's crucial info missing.

I've been together with my girlfriend for a year and 5 months on the dot at the time of posting.
She's the most amazing, beautiful and loveliest girl I have ever met in my life. She truly has the looks, the brain and the wit all in one package. to stop me from further babbling i'll just say that she's perfect.

We're both still in university: I'm finishing up my masters this year and she has still a few more years to go. We have been living together for 4 months now, and with that I mean that during the week we're living together but during weekends and holidays we still go to our parents. It's how people do it where I live.

That describes the situation, now the part where fuckups happen:

My girldfriend has HSP (not some self-diagnosed-internet-quiz-BS but real proper medically tested HSP) wich means she's really suspectible to external stimuli that alter her mood. To me this is no problem, I love her all the same no matter what. but the problem is: I think i'm totally handeling it wrong which has a negative impact on her.

example:
We've been planning to take a cat but yesterday the landlord met our request with a flat-out "no".
She started crying her heart out. I huged her, provided her with tissues, told her i'd try to reason with the landlord (as not allowing small animals is actually illegal). In the end she cried herself to sleep in my arms.

This morning we wake up and she's acting cold as ice. I suspect this is some defence mechanisme to protect her from further emotional harm. She tells me she's going home for the rest of the last week of the semester as she can't study here and probably will stay home to study for the whole month of January aswell (this is the exam month).

This is where I think I fucked up the most:
I'm a rational guy so I respond, after a minute or so getting to grips with it, that I will miss her a lot but that if she thinks she will study better at home that I understand and that she should do it as her grades are really important.
Maybe is hould've asked her to stay? but that'd be so selfish and I really want her to have good grades. Tbh, I have no idea how I should've handeled it.

When getting ready to leave (she had somewhere to be) she didn't allow me to hug or kiss her and didn't reply to my farewells. So here I sit, writign a reddit post worrying about her.

Anyway, she left for the day and because she's not comming back next week I won't see her till the 31ste for NYE. I'm scared I might've fucked up beyond a simple apology. This is often how things go: soemthing bad happens that'sby no means my (or her) fault and all of a sudden my efforts to comfort end up in her being cold. Note: I'm by no means blaming her for anything, i'm 100% sure she's handeling it to the best of her abilities and I admire her for it. I just wished I could help her, prevent her from going into that defensive state?

TL;DR:
Girlfriend is susceptible to extreme moods and protects herself afterwards by giving me the cold shoulder. I want to help her but fail every time. Failed attempts might be worsening it and i have no idea what to do.