Hi and thank you, too! I love the horror genre and horror sound design in general, maybe I can help, here are some suggestions :
You want to record vocal rises at different speed and layer them, these will create random clusters and harmonic dissonances.
Also do vocal rises that end in nasty screams.
As additional material I would suggest screams without rises just like girls scream in horror films, more like impacts. Of course any noise you can make, may serve as basis (hiss, grunt, growl etc.)
When layering your voice you will run into harmonic problems, because the typical frequencies of your voice will be doubled over and over again and saturated. So vary the space (reverb setting), pitch them down and up, change speed artificially afterwards. I have done this with violin rises I have recorded myself with my violin, worked pretty good!
If you want to get more into technical rises, you have to create very short loops of your voice (or not so short depending on how it sounds) and create a larger pitch envelope upwards. It sounds easily synthetic, so be careful, in horror sound design, we usually want it to sound "organic". Again layering different rises may be interesting.
To do this you can also try other material, in example a hiss. A hiss naturally can't go up, but with this technique it can. Try to keep the natural sound of the hiss.
One last trick I use sometimes is to "sweep" through the spectrum with a filter. The frequencies "high lighted" get higher and higher. Of course you need a rich source sound for this (scream?). Here also it can sound quickly artificial so be careful, to not go too fast.
Hope this helps!