Is there really a virus that can do this?

A virus can do this, or at least make it look like that. You did not send her anything, but the virus would have access to her contacts list, and hence your email, and could make fake mails look like they came from you when they did not.

It was a real email of mine that she read. It was sent to someone she does not know and had no connection to her.

I’ve never heard of that – my first thought was what @poisonedantidote described. But a virus on her computer should not give her access to emails that you wrote to others. Were you all using the same email provider (i.e. gmail or hotmail or what have you)? Or is it possible that the email might have forwarded to your friend, perhaps via multiple other people? Finally, is it possible that you have the virus?

Hypothetically speaking, if you had ever logged onto your email on her computer, there could have been a keylogger and that can give them access to your email account.

But if you haven’t done that, and assuming that your computer hasn’t been compromised, there’s always spoofing. People can put fake email addresses, just like they can put bullshit “Return to” addresses on a snail-mail letter. (Wikipedia article)
In some cases, it’s not even nefarious. Like meetup.com, when a group leader sends out a mass email through the system, it’ll say that the email is from the group leader’s email address, when really it’s sent by meetup itself, and it didn’t have to get access to their email account at all.
But in other cases, it can be mischievous or downright nefarious.

I would ask her what kind of emails they are. Are they just obnoxious? Or are they linking to questionable sites, or asking for sums of money, or what?
And I don’t think there’s anything she can personally do, but she should report the issue to her email service, they can handle it.

I did log onto my email at her house once and she had mentioned that she had some sort of virus. She also has a key logger to track her son’s internet use. That doesn’t explain why she also received emails from her friends in California who have never been to her house.

They were real emails that I wrote to people, not spam. It seemed she basically received what was in my inbox, which included some addressed to her and many others that were not addressed to or associated with her in any way. We do not use the same provider and she says her other friend uses the same one she does.

My computer was definitely clean.

She read an email that ended our friendship. I have felt guilty for over a year about this, but now I am wondering if she didn’t log on to my account (maybe access through above mentioned log on at her house?) and just said she also received similar emails from two or three other friends so it wouldn’t seem suspicious.

Wow. My guess is that your suspicion is correct. That sounds like the most likely explanation by far.

I am not aware of a virus that could do that, or how it could.
I am betting you are correct.