Kirsten, I'm sorry not only for the loss of your friend but for the stress and struggle you are going through. The last thing your mind wants to do right now is something "good" for you (eating) because you are hurting. You will be physically hurting even more if you don't eat, honey. I've been there (not with the loss of a loved and dear friend, though) and the only words of wisdom I can offer are you know the
right things to do, I can tell from your post by saying your friend would want you to take care of yourself, just hold tight to the good memories of your friend, come here for help if you need it, feel free to message me anytime. Don't feel bad about missing the funeral, you can celebrate her life anytime, anywhere (and that's what funerals should be); her spirit and soul are not where her body is, those are with you.
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"We can't talk at the same time! It doesn't work like that! I talk, you talk, I talk, you talk!!" ~ Peanut