I'm really sorry to hear about this. Hope you're feeling ok.
The obvious thing to do is offer your condolences to the family, turn up at the funeral and so on. Sending flowers is nice but by no means essential - they probably have bigger things to worry about than who sends them flowers. Don't worry about all that. Deal with mourning her death in your own way, and if you feel capable of doing so, let the family know that if they need anything, you'll be there to help them. But it's perfectly natural to feel that you can't, and don't feel obliged to strain yourself over traditions and formalities - the chances are they will barely notice if you don't, and if they do notice, they'll understand.