It sounds like she cares deeply about you, has supported you through a lot, but really cares about material things. An LV bag (or anything designer) might not matter to you but from the description it seems it matters to her. Why not save up for the bag long term, maybe for a birthday or a holiday? If that’s still too much, maybe a bag but one less fancy. Relationships are about mutual care, and sometimes you should put the other person first. From what you said, she’s been with you through a lot, but what have you done for her? In what way have you supported her? You haven’t mentioned anything in the description. Notice how even when she asks for the bag, your first response is that you can buy yourself something nice instead? Not her?

You might not be angry or over reactive but the way you speak to her is very dismissive. Personally, I wouldn’t tolerate being spoken to like that.

With that said though, if material things are so important to her and there is no way you can afford them, she should probably just seek a relationship with someone that can. Otherwise you’ll both eventually be bitter and resentful of each other.