If you were coming to Doctor George as a client, he would start by having you explain the situation, as you did in your letter. Then, rather than discussing all of your questions, Doctor George would only address the most important aspect of the conversation, leaving the remaining questions aside. That's because our understanding is built on fundamentals, one layer at a time. We usually need to have a solid footing on one layer before we can understand the next. This is difficult to achieve without more personal interaction, as would be present in a counseling session; but, nonetheless, Doctor George is going to try to answer your question using the same process that he would if you had come to see him in person.
There are three aspects Doctor George would want to explore...
The first aspect, that Doctor George would address, would be your initial behavior. Was it appropriate for you to secretly see your former best friend's cousin without her knowledge? Was your friendship one in which the disclosure would have been appropriate, thus making your failure to disclose your actions a legitimate betrayal? Or, was it unreasonable for your best friend to expect that you would tell her? Or, were there other mitigating circumstances? For instance, did her cousin specifically want the relationship to be kept private and not discussed among his family?
The second thing, that Doctor George would address, is your friend's reaction. When someone feels wronged by us, we don't get to vote on their response. The fact is that they do feel how they feel, and we have no right to expect otherwise. If we did something to cause or inflame those feelings, we need to accept our responsibility. Doctor George would not address the specifics of your ex-friend's response, as much as he would your acceptance of it.
Thirdly, once we addressed what you did and accepting your ex-friend's response, we could then get to your response to her reaction. Just as your friend has a right to respond to what you did, you have a right to respond to her reaction. By going through the process properly, we could determine whether your reaction is legitimate -- as in you believe you behaved appropriately, given the circumstances, and that your ex-friend overreacted -- or whether your reaction is not legitimate, as in you know what you did was inappropriate and you're trying to avoid being responsible for it. Whatever outcome you achieve with your friend is less important than your internal resolution. Even if Doctor George provided the specific answers to the questions you asked, it doesn't mean you'd be resolved. It also doesn't ensure that similar situations won't arise in the future or that this situation isn't similar to one you experienced in your past.
Obviously, Doctor George doesn't know all of the circumstances surrounding your being with your ex-friend's cousin. Perhaps it was legitimate and your former best friend was imprudent to act as she did. Another possibility is that you felt entitled to do whatever you pleased, regardless of how it affected your best friend. If that was the case, Doctor George would talk to you about entitlement, including being with your best friend's cousin, feeling entitled to keep it from her, feeling entitled to receive the response that you deemed was appropriate for the transgression, feeling entitled to determine how she should behave, and feeling entitled to forget about it without having a proper accounting.
As stated, Doctor George would need to discuss it further to determine whether entitlement is at the heart of your behavior. You asked, "How can I get rid of these emotions?" That could be interpreted as an attempt to bypass the consequences of your actions and forget about what happened -- in other words, entitlement. Further evidence of entitlement is perhaps revealed when you say, "I feel this discomfort and lack of peace within myself." That's an entirely different situation than being annoyed at someone else. In the end, it leaves Doctor George wondering whether you are asking the right questions of him and of yourself. Perhaps you should really be asking why you are not at peace rather than focusing on your being annoyed.