If it appears resolving a claim for fair compensation without a lawsuit is impossible, then a lawsuit is the next step. The lawsuit should be filed as soon as possible. Priority #1 is getting healthy and recovering from injury. You have 3 years to file. After 3 years (the statute of limitations), you’ll have no opportunity to get compensated for your injuries.
That doesn’t mean you can procrastinate and wait 2 years, 7 months to file a claim. The longer you wait, the more evidence slips away—and you lose leverage.