Hazel,I am sorry for your loss, you have my prayers and deepest sympathy.
I'm sure your grandmother would understand and want you to be okay. She will always be with you in your heart and memories.
If you cannot go, do not feel badly as you do have an anxiety disorder as well as many other things stressing you right now. It's not like you don't want to go, it is the fear of traveling alone, and the GAD that are causing you to stay at home.
Give yourself permission to do your own memorial for your Grandmother at home and do not get caught up in guilt.
As far as your Mother, thank her for the offer to pay your way, tell her your sorry you cannot come but let her know that your Grandmother was a very special lady and she will always be remembered by you.
In the end, nobody knows but you how you will feel after the service if you do not go so do what you feel is the best for your health.
Prayers,
Kitt