As a practical matter, yes, you do. Technically, a person can try to do without a lawyer, but that is always a terrible idea. Hiring an attorney to represent you after a slip and fall accident is the only reliable way to obtain the full compensation you deserve. Otherwise, insurance companies string injured victims along, deny claims, and make unreasonably low settlement offers.
An attorney protects you from these tactics, investigates your claim, builds the strongest possible case, negotiates with insurance companies and defense lawyers on your behalf, and takes your case to court when necessary. Do not make the mistake of thinking you can handle those tasks on your own. You cannot, and trying will cost you time and money that you cannot afford to lose.