Your options are either for her to want to get help, then go through a long process of counselling and therapy to understand why she reacts so badly to sex, and then to move past it, or to accept you two are incompatible and move on.

Given that she's absolutely rejected the first option you have two new options: a miserable life half-lived ('cos brother, sex with a willing partner is the freaking best, and all the extra actions like oral, touching and so on are like the best icing ever on a sweet-ass cake) or move on and find someone who can actually fill, or even try to fill, your needs.

She's shaming your sexuality because she knows you have needs and is scared to lose you (which is perfectly normal in response to her own refusal to seek help for her condition), but it's also a selfish thing to do. If she knows she has no interest in sex and never will, the reasonable thing to do is to seek out a partner with a similarly non-existant interest in sex, not to try and make a person with a regular and healthy sexual appetite feel bad for his perfectly acceptable needs and desires.

First, you need to accept that you are not wrong to have these needs.

Second you need to accept that she is not wrong to not have these needs, and also not wrong to not want to change - but she is a little selfish to not want to change.

Third, you need to have a conversation with her where you inform her that she is perfectly within her rights to refuse to even try and get help, but that you will not feel ashamed for having a normal sexual appetite, and it is wrong of her to tell you to 'just go without'. You should probably then break up with her, for both your sakes. She cannot be happy knowing that she can't fulfil all your needs, and you obviously aren't happy. When neither partner is happy and there is very little to no chance of compromise on the issue in question, the relationship should end. Sorry dude.

Or, you know, castrate yourself. Which is obviously ridiculous, but that's about your only option when you talk about 'making yourself less horny'.

Good luck.