Opening a retail garment showroom in IL
From wikipedia this is what I read about H-4 visas:
H-4 visa holders are not eligible to get a Social Security Number and cannot be employed, but they can hold a driver's license, open bank accounts, and get an Individual Taxpayer Identification Number for US tax purposes.
So although you could form a company in the US and be listed as the owner, legally you would not be able to be employed by your business.
I would recommend you to consult an immigration attorney to see what options you have to obtain employment authorization maybe through your business.