Other driver’s insurance wants a recorded statement before they’ll even look at my injury claim

Got hit last week and the other driver was pretty clearly at fault. Their insurance called me and now they want a recorded statement about what happened and how I’m feeling before they’ll really move forward with the injury side of the claim. I’m still getting checked out and don’t even know the full extent of everything yet, so I’m not really comfortable giving some detailed recorded statement this early. Been looking at crashhelp because I’m starting to think I should talk to a personal injury lawyer before I say the wrong thing. Is this a normal part of the process?