Trying to Mend Fences

I work with a woman who, how can I put this, hates my fucking guts. Without going into too much detail, we were friends for about a year before I was diagnosed with cancer. We're both married. After I was diagnosed, she was very supportive and was someone I could talk to, she was studying to be a psychologist, and our friendship was going ok. I crossed a line and became emotionally dependent/attached to her. It imploded on me and I said something I shouldn't have (nothing nasty or vulgar) the chemo and steroids and the stress of everything got the better of me. She basically told me to 'fuck off'. Anyway, I've been getting the staring through me thing for about a year I guess. I almost physically ran into her a few weeks ago and out of a reflex said "Hi", I got nothing back at all except a cold stare. It bugged me because although she accepted my appology for what I said to her, I know she never forgave me. I brought this up with my therapist (my wife also knew what happened, I told her at the time and she understood) and my therapist asked me if I forgave myself, which I feel I have. If anyone's gone through cancer they may understand, it's an incredible mindfuck. So I/we have been avoiding each other for about a year. We work in the same department but in different aspects of production so we really never had to interact. Well, as fate would have it, we are both on the same project and we have to attend meetings together (in the same room at the same time). It was terrifying for me at first because I did not want to be in the same room as someone who I feel hates me, but my manager asked me if I wanted to attend the meetings representing our group and I said yes. I figured it was time to face the music. There was an 'negative energy' in the room, but it wasn't very noticeable. We didn't have to interact with each other so I survived the meeting. I've been to maybe 5 meetings so far. Yesterday I was there and 'my friend' had a wicked sniffle. I mean, she was sucking up snot like a 3 yr old. For one, it was annoying and I could tell she wasn't too comfortable either. I had to go to use the restroom and on my way back, I was able to find a box of tissues. When I came back in, I placed them by her and said something like 'it sounds like you could use these'. She either said 'Thank You' or Fuck You'. I think it was the first one and not the latter. When the meeting was over, she again said one or the other and I said 'not a problem'. I would have done that for anyone, but since it was her, it took a little more courage to make the move so to speak. I know this is not going to make things better and it was not my intention when I went to get the tissues. I just want to have it so it's not uncomfortable for me and I would really like it if she one day forgave me or at least understood what I was going through at the time. I try to be more careful who I confide in now. Most people really don't want to hear my cancer and I can't say I blame them...
...time will tell if she forgives me, life goes on.