Hi, I'd like to help you with your question.
It sounds like you are an honest person and lying is not second nature to you. It is sometimes necessary to mislead someone because of good intentions. When it can be explained later, it is ok to mislead. That is the difference between someone who outright lies for their own benefit and someone who does it for good and the eventual truth.
Your girlfriend questioned you and to try to hide what your true intention was, you made up something on the spot. Since you are honest by nature, you tried to find a lie that was misleading to her so, like you said, she would not suspect you might be shopping for a ring. But when she suspected you were misleading her, you made up a lie closer to the truth. But because the reason behind your lie is not apparent to her, she now feels she has the basis to mistrust you.
The ring situation will work itself out when you give it to her and explain what happened. When you are faced with a situation like that again, try to think ahead. What would happen if...? kind of thing. This will help you sound more credible and she won't see through it so well (as long as you have good intentions!).
You can repair this with her by telling her you love her. Let her know she can trust you and you have no intention of hurting her. Try to avoid bringing up the incident itself but if she brings it up anyway, tell her that you are asking she trust you this time. Let her know that you take her trust very seriously. Let her know you hear her concerns and understand why she feels the way she does, but if she can just trust you on this, it will be ok. Reassuring her should help her.
I hope this has helped you,