slip and fall accident in costco, procedure for filing a claim

If you are injured, the first thing you should do is seek further medical attention.

It is probably worth seeking the advice of an attorney, as slip and fall cases can be difficult to pursue. Reason being is that you have to prove that the entity had either actual or constructive knowledge of the condition (in this case, the chicken grease).

To fuly answer your questions more facts are needed. However generally a landowner or Operator such as Costco owes a guest both a duty to warn of known dangerous conditions on its property and to maintain its premises in a reasonably safe condition. Since you say that grease was all over the area you can likley expect a defense of an "open and obvious" condition which may result in a summary judgement against you if the condition should have been seen by you. However if you aslo sue on the basis of the second duty- a failure to maintain its premises you can win because the store personnel should have seen the spill b complying with what are likely written policies and procedures regarding regular inspections, sweeps of the store floors and logging of the times of these :sweeps"
Your case value depends upon the sxeverity of your injury and must be evlueted by an Orthopedic specialist as soon as possible- injuries can develop over time, but large delays in treatment hurt your case later as it appears as though you were not reriously injured enough to see a Doctor until you consulted with a lawyer. get checked out now to give you peace of mind or know if you have something more seriously injured, then you can decide to consult with a personal injury attorney in your area and decide toghether if your case is worth pursuing.