I know that's very hard. You're friends. You have a deep, long, and rich friendship, not just some surface thing. One of the hardest things I've found between my own friendships can come when one friend finds herself in a better or worse economic status than the other friend. I've been at both ends of that equation, and it can be very uncomfortable. It's like suddenly, you have to be very careful about what you talk about. I've felt the envy of wishing I had the money to take my kids on a trip after hearing about someone else doing it, or to do expensive upgrades on my home when a friend is deep in the throes of remodeling and talking about the details--as friends do! I've also felt the sudden withdrawal of friends when either I came into some money--or they lost a job or a husband who provided income--and I ended up being the one with higher financial stability than them.
When we are all in a situation where an international economic crisis has led to personal concerns and sometimes real tragedies for many people, it can be hard to remember that we are friends first and foremost, and to stay that way as things shift. I think it's important to be sensitive to your friend's situation and why she may have acted the way she did. I know what she said hurt you, but you WERE listening in to a private conversation that was not meant for your ears. That may have been her way of "venting" her feelings so she wouldn't take them out on you, when you didn't deserve it. It wasn't nice. It was hurtful. But you took her off guard when you "confronted" her about it, and that doesn't bode well for de-escalating the problem.
Here's what I would do:
Either call her, if you think she will listen, or send her a card with a handwritten note.
-I'm sorry. I was insensitive about how tight things are financially for you right now, and you didn't need to hear me talking about my new ring. I should have realized how that might feel.
-I miss you. Your friendship has been a very special part of my life for a long time. We have shared so much. I want to stay your friend. I want you to stay mine.
-I was hurt by what I overheard, but it wasn't a conversation for my ears, and I shouldn't have listened.
-I care about how you feel. I am concerned about how you are doing. I don't know how to be when, right now, we aren't in the same place financially, but I want to make sure our friendship evens out so you get what you need from me as a friend and I am able to still have you as a friend.
-Can we please talk about this?
What you SHOULDN'T do (and believe me, I know how hard this is, and I DO understand you are hurt by what she said) is try to get her to apologize for what she said. Make the communication all about opening your heart to her and what YOU could have done better. It's very likely she may come to a place where she apologizes on her own, once she hears that, but it is not likely at all that she will apologize if you ask her to--no matter how justified you may feel.
I think a friendship is worth swallowing your pride over and trying openly look for your part in it. I have personally saved a friendship such as this, by doing exactly what I've suggested.