Consider rutilated quartz, particularly if you can get a small sphere. I think the "organization" of rutilation will help immensely because you will be getting a visual affirmation about how it is possible to be schitzo yet stable.
While many stones will be good, I think those cut in spheres and cabachons will be particularly soothing for you. Beads would be excellent too and you can make up a nice bead string that is meaninful to you. I can't imagine not touching my stones when the going gets rough.
I certainly agree with the suggestion about amethyst, but may I give agate a plug? It's beautiful, inexpensive and so so centering. I really think it is undervalued because it's not a rare stone. There are so many different types too.....picture (usually brown-ish), dendrite (like pictures of moss), blue lace, etc. Since you are dealing with an disorder that makes you fragmented, the qualities of agate will help pull you together. Geodes are good for this too.
BTW, you can get a bag of agate marbles for next to nothing. Just google up "marbles"