Not filtering on categories?

I have a B2B shop set up for tires.

I have parent categories and child categories like this:

Width
-> 255, 265, 285 etc.
Height:
-> 55, 65, 75 etc.
Inch:
-> 15, 16, 17 etc.

I also want the ability to search in a box, example if you search for 255-65-15 i want the tyres in that categorys to be filter out. But i can not get it to work?

Any ideas?