Living in Ohio, website creation is not taxable. If I build a website for a business in another state, should I be collecting taxes on it and will I be taxed when I file?

I do web development in Ohio as a self-employed side business. I am a registered LLC but I am a sole owner there is no other employ. I don't charge taxes but am receiving a 1099 paperwork from a business that pays for my services and they are out of Florida. (again I live in Ohio) When I submit that 1099 paperwork, will I be able to declare that it's web site creation services and not get taxed or will they hit me with taxes even though in Ohio it's not taxable?