Should I cut the lady I mentor off?

I went back to work in June of 2020 after being a SAHM for 6 years. Long story short, I've been killing it. I'm a third party contractor and the site I work at has taken notice of me. They have asked me to apply for an open spot in a leadership position that would be a huge pay increase and would really be an amazing opportunity professionally as well as help me to do better for my family. Heres where the problem comes in to play, I made friends with someone who joined my crew several months ago. She's younger than I am and has really looked up to me. I've been sort of a mentor for her. I took her under my wing and attempted to mold her into a better employee. We became really close. Spent a ton of time together outside of work, lunches, kids playing together, dinners, etc.. anyways she heard about the job opening and let me know last week that she was going to apply for it. When she told me that I told her that I was also applying for the position. I thought that it would be better to let her know I was going for it than to hide it from her. She responded with a short one worded response and then a few hours later I saw her post on her Facebook some passive aggressive thing that was obviously directed towards me. A mutual friend of mine, who was aware that we were both applying for the job, told me that her post was absolutely directed towards me. I decided to message her and ask if she was upset that I was applying for the job and if her post was about me, she assured me she was not upset and that the most was definitely not about me. I wasn't convinced. Later that night, our mutual friend called me and told me that he had spoken to her and she was livid over me applying for this job because she knows they're going to give it to me over her. I am more qualified, more capable, have more experience etc.. I have no doubts that I'll get the job over her. However, if they did decide to give it to her over me then I would be happy for her for trying to make a better life for herself. She told my friend that I'm being spiteful and selfish and am only going after the job because she wants it. I've never given her any reason to think I would try to do something like that. She thinks I should back off because she needs it more than I do. She doesn't know that our friend told me what all she said. She's still acting like everything is fine between us. I've already come to her and asked if she had a problem with me applying and she denied it. I saw that she deleted that post that she claimed was not about me. I'm very hurt that she's making me applying for this job all about her and taking it as a personal attack. I'm hurt that she's saying these awful things behind my back. I'm hurt that she's making herself a victim of some attack. She really thinks I'm in the wrong for trying to get this job that I truly deserve and have worked hard for. Do I just write her off and move on? I can't stand this two faced drama. Being my friend to my face but just dogging me behind my back and outright denying it when I approach her about it. What would you do in this situation?