Sending love and compassion OP. I could have written this post myself a couple of years ago.
I don't really know how you can accept something that is so ambiguous, you seem to think that you not being beautiful is a fact, however I can 100% guarantee you that there's someone out there thinking this exact scenario about you (yes I know you just completely brushed that off as not true) because of course YOU know that you are not beautiful and this other woman IS beautiful. Beauty is in the eye of the beholder, a flower and a rainbow look completely different but I find them both beautiful.
I remember a woman who I thought was incredibly beautiful, I didn't know her personally but she was local and I saw her quite a bit. One day my friend mentioned her as she was a beautician and my friend had received a treatment from her, i gushed oh isn't she so pretty! My friend looked at me like I had two heads genuinely shocked and said do you think? I said don't you? She said no not really, she's just average never really thought of her like that. I was so shocked I assumed that EVERYONE would think she's incredibly beautiful because I did.
Similar things have happened about people on tv I've not found remotely attractive and my friends have thought were stunning.
I'm not saying this woman you're referring to isn't beautiful, but it's not black and white. Beautiful/ not beautiful. It's a spectrum and it's often a preference or taste.
You said you don't want other people to think you're beautiful but to be able to see it yourself (I'm paraphrasing) you're assuming that woman you think is beautiful sees herself as beautiful. I'd put money on it she doesn't. I've known and know many beautiful people male and female and not a single one of them thought that they were.
Beautiful people still suffer from insecurity, jealousy, still get cheated on, still have self esteem issues. It's not a golden ticket.
I understand your frustration and sadness, I've been there myself, what helped was putting less importance on it.
The sad thing is you will look back when you're 80 abs realise you were beautiful all along and wish you hadn't wasted any precious minutes of your life worrying otherwise.
I hope you find a way to feel better, therapy definitely helps.