OMG, please listen to me. Good people like you and your girlfriend have so much love inside them that they are able to love someone even when that person is very, very bad for them. It's kind of like loving a food that you are allergic to and that can kill you. Being depressed is the worst possible thing that two people can have in common in a relationship. She is probably the worst woman in the world for you to try to have a romantic relationship with, though she could be a great friend.
There simply isn't going to be any way for you to have a satisfying relationship with her, ever. Her mental problems concerning sex won't go away, and more new ones will develop. If you marry her, she will withhold sex from you as much as she can, and even when you do it, she will make you feel that she doesn't want it. She will constantly be accusing you of things and your life outside of the bedroom will be miserable too.
The only way to have a healthy relationship with her is to just be friends. You can be friends for life. Your girlfriend should probably never have sex with anyone. It's too emotionally charged for her, and if she does it, those feelings will multiply a hundred times. She might even harm herself because of it. Remember, women are given a lot of negative messages about sex, but only a few of them believe it and make that negativity a part of themselves. Without sex, she has the potential to lead a happy life.
You, on the other hand will be able to have an incredibly intimate relationship with a woman who likes sex and for whom it is a beautiful bonding experience. You'll probably even be able to have enjoyable casual sex with FWB. You have your whole sexual life ahead of you. The only thing that is stopping you from finding the right people to be friends with and to be your spouse, is your completely dysfunctional relationship with your girlfriend. You don't need to stop loving her, if the love you feel for each other is real, it will last even if you are just friends. I have experienced this is my own life, as my best friend now is someone I was in a romantic relationship with for five years.
When you break up with your girlfriend, you will feel sad for a little while, then something magical will happen to you. All of a sudden, it will be as though a great weight has been lifted off you. The feelings of love you hold inside will open at once to everyone and you will feel excitement at the prospect of getting to know new people. You will become more outgoing and will make new friends.
Your friends will help you meet women to date and from them, you will find someone who feels the same way about sex that you do -- that it is an exquisite expression of intimacy and love. Only with someone like this, will you be able to find fulfillment in a relationship. Never forget that, and don't ever settle for someone who has any negative feelings about sex. It is much better to wait for the right person. Look on this sub for "red flags" to see some of the things to beware of when you are dating someone.
Over time, you will learn more about yourself and, without your current girlfriend's negativity holding you back, you will start to feel better about yourself. You will gain self esteem. You will learn to love yourself more. I'm very shy and have suffered from depression since I was a child, but I recovered from every break up in my life and now have happily been with my SO for 20 years. You can do it too! Hugs!