Is the problem she cannot "be around" wool, or handle wool and cannot sew a coat up, or is the problem that the coat is intended for her to use and she cannot wear wool?
While there are wool/nylon blends that can be found in the 80/20, 85/15, 70/30, and even 60/40 ratios at times... wool, kersey, and flannel look like wool, kersey, and flannel.
Yes, there is say green cotton, but cotton does not appear as, or "look like" wool, kersey, or flannel.
On the other hand, in some circles the "standard" for Berdan uniforms is overly heavy 22 or 24 ounce "blanket wool" which does not "look much like" Period Berdan coats.
Others' mileage will vary...
In gleichem Schritt und Tritt, Curt Schmidt
Not a real Civil War reenactor, I only portray one on boards and fora.
I do not portray a Civil War soldier, I merely interpret one.