First of all, let's cover what you don't need. What you don't want to do – ever – is to sign a document that the company puts in front of you immediately after you've been injured. In many cases this is what happens, and the company throws paper at their injured worker and before they know it, they may have signed away any rights they had to make a claim under the Jones act. This needs to be avoided at all costs, and is why you should always consult a lawyer who specializes in Maritime Law before you sign anything the company puts in front of you.
What you will need in terms of paperwork is medical records. Your attorney can handle the rest, and sometimes can handle getting copies of your medical records as well, but it is vital that you obtain as detailed copies of all relevant medical information as possible. This means much more than just a doctor’s note, and includes things like X-rays, lab results and the results of any scans or tests which are done that prove the extent of your injuries, as well as the costs being incurred for medical treatments. You are going to need to make sure that your lawyer receives a copy of all of this documentation, and you should also try and keep copies for your own records in case you run into any discrepancies down the road.