What about this:

You could have asked me out yesterday. I know I was sick last week, but I was able to go out last night.

Is it possible?

As a first approach, I would play it safe: You could have asked me out yesterday. I know I was sick but I could have gone out last night.

It seems it does not matter whether the person got better or not, she didn't go out anyway, we are talking about something that is impossible to retrack.

Now, the unspoken/unwritten will always be bound to the situation , and then we can only infer, image or try to recreate; it might the case that the speaker got better or was willing to go out no matter how bad they were.

JR