My gf (F19) is mad at me (M18) that I did not reach out for her after she had blocked me, and is under the impression I do not care about her. How do I reassure her that I care about her and love her?

For context, since the start of our relationship (7 months), my girlfriend (let's call her V) has not been too comfortable with me hanging out with my best friend (F18, lets call her F) that i have known for 4 years, e.g. hanging out in central with my friend. V tells me that she knows I'm not doing anything with F behind her back, as our friendship is purely platonic, and i've introduced them to each other before, yet V is still quite uncomfortable with me seeing F. I told V that i am seeing F in a few days time, as i havent seen her in 2 months at this point (I see V everyday at college), and she was okay with me hanging out with F if i told V in advance. I let her know when I am leaving, what we are doing, and told her I would update her. On the day of going out, my family told me they had also planned a picnic in a park, very close to where me and F were going to be hanging out. I let V know that me and F are going to see my family as well as apart of the hangout, and I even invited V to come with us too. F has known my family for years, so i assumed it was nothing out of the ordinary. After i had told V this, i noticed that her profile picture on Whatsapp, and her location was gone, alongside only being able to send messages with one tick. From here, i realised i was blocked, and i decided to wait out a few days and spend time deciphering the situation. I decided to not attempt contact her on Snap (the one platform she has not blocked me on) out of respect for her privacy, and for my self respect. Fast forward a few days, i see her back in college, but she is cold with me, giving one word responses to questions (like 'how have you been', 'is everything okay' etc etc) I asked V if we could talk and she said nothings wrong, and walked away to her next lesson. The day after that happened, i found her sitting alone, and i made it clear I know she is upset with me, and i want to have a conversation with her about it, to fix things from my end and understand how she feels. She started by getting mad at me, questioning why I did not contact her at all. I told her it is because she had blocked me, but V responded by saying 'so what, my snapchat was unblocked, if you really did care about me, you wouldve went through that workaround of contacting me on there, and because you did nothing, im under the impression that you dont care about me or love me at all'. I responded by telling her i do care about her and love her, but it came off that she did not wanna talk to me at all by blocking me, and that she didnt expect anything out of me. This made her more upset, because she was mad that I was assuming that was the case, and i shouldve asked her regardless on snapchat if i should talk to her (I sometimes assume things wrongly, which greatly upsets her at times). I told her that when things like this happen, we should talk about it together maturely, instead of having a case where one person gets shut off and has to chase each other. She got irritated by this comment, saying that i am the one at fault here, and that she does not need to do anything at all. She told me in January (after an argument), that if she goes cold with me, that i should at least 'do something', to reach out regardless, or get her interested to talking to me - something along those lines. I felt guilty about forgetting about that, and I decided to take the blame on all of this at the end, and promised her that i will be better. We are on a break from our relationship right now, and is thinking about whether she should continue this relationship or not. I want to be able to convince her that I really do love and care about her despite of how i made her feel, and i want her to also understand how i feel about what i felt, - how can i do so? TL;DR: Gf is mad at me for not reaching out to her on a different social media platform after she blocked me on our main platform, and i took the blame on it.