No matter what life deals us, and no matter how angry we may feel at matters that we cannot control , it simply isn't fair to take our frustrations out on others.
Instead of snapping, you could have changed the subject or confided how you were feeling. Instead you have needlessly alienated someone who has already demonstrated that she is a supportive friend, who has the ability to empathise with your grief.
Write a heartfelt letter to your friend and apologise sincerely for taking out your angst on her. Say that you appreciate her suggestion which you will act on as soon as you can work through the anger you are currently feeling.
Also say that you deeply appreciate the support she has given you, and that you hope your behaviour hasn't ruined a friendship that you have come to greatly value.
You may feel that you have 'started the grieving process' but nothing can prepare you for the grief you are going to feel at the eventual loss of your mum.
While it''s all very well 'leaning' on others, it can be harder to learn how to stand up straight and cope alone if the prop falls away.
Realistically, there is only one person that you can rely on in this world and that is yourself. Make a vow to honour your mum by behaving like the well-mannered, considerate, caring, adult she raised you to be - and always deal with your anger in private or vent it here.