You are overreacting. I am also not a tactile person and can not cope with these
Interesting problem to have. Usually, if someone complains their partner finishes too fast for their pace, it's the woman who is complaining. If the man is slower to reach climax than the woman, a lot of women might be able to keep going because they can keep having orgasms along the way. (Unless the area is too sensitive for her after one orgasm to be able to stand more.) I'm also a bit surprised at you calling 10 to 20 minutes to reach orgasm "very fast," if you mean 10 to 20 minutes after penetration. A lot of guys come to orgasm in five minutes (or less) once inside. For many men or women 10-20 minutes of continual pumping towards a happy ending would be too long. But, you are the way you are, and she is the way she is.
If she doesn't want to do missionary or side-to-side options, then you two should certainly discuss (without blame or shame) why not. There might be pain or sexual trauma in her past that makes it impossible for her to have sex any other way. I don't think you are over-reacting -- after all, sex can't be entirely unsatisfactory or the relationship won't work -- but I don't think she's being "selfish." She sounds like she is doing what she's doing for a genuine reason, which you are better off to address with sympathetic interest than complaints that she's selfish.
After discussing it (I hope with a counselor's help), if you can't work out a solution that does the trick for you both, I'm afraid this might be one of those deal-breakers that cause people to not be able to stay in a relationship. i hope not. See if you can find a therapist that specializes in sexual issues, to talk it over and not just quit.