Did they ever count as a relationship?

Several years ago two of my friends at the time hooked me up with with a friend of theirs. I always looked back at my very short time with her as a relationship, but I wonder if it is or not, now in reflection.

We went on a date and I pretty much drove to her place later that night and we fucked. After that night we pretty much spent time together almost all the time. I think by the second week were talking about love or something and I sort of asked how she felt about me, and she said “I think you know the answer to that.” I felt the same way too. I started getting upset that we spent time together so much and tried setting up boundaries, but she wouldn’t listen. I tried being less available so I could have more time for myself. She eventually FaceTimed me and suggested maybe we should just be friends, and that upset me and didn’t want to just be friends. I think we met up sometime after that to make up or something. Despite this, she still wouldn’t give me my space and eventually we FaceTimed again, and I said “ Let’s just break up” or something along the lines of that. She was shocked and couldn’t believe what I said.

I should mention all this happened in the span of only a month, so that’s another reason why I ask this question as if time determines a relationship or not?

Edit: Title should read “Did this* ever count as a relationship?”