Driver who hit me is now asking me to lie to insurance — do I save these messages?

Screenshot everything immediately. Voice note, texts, timestamps, all of it. Back it up somewhere you won't lose it. Yes, absolutely give it to your insurance company — don't editorialize, just say "I received these messages after the accident and wanted to make sure you had them." You're not accusing anyone of anything, you're documenting. That's your job right now.

I worked claims for years. When something like this comes up and one party has documented evidence that the other asked them to falsify a statement, it very strongly establishes who's acting in good faith. Hand those messages over. It actually helps your claim more than you might realize — it shows you're the cooperative, honest party. Adjusters notice that.

Also heads up — even if YOU do everything right, be careful that the other driver doesn't get ahead of you by calling their insurer first with some alternate version of events. Get your recorded statement in early, stick to the facts, and let the documentation speak for itself. Don't assume honesty wins automatically without you actively protecting your own account.

Something similar happened to a family member of mine — the other driver tried to "work it out" off the books after the fact. My family member felt guilty saying no but ultimately reported everything. It was absolutely the right call. You got hurt. Your neck and shoulders are real injuries. Don't absorb someone else's consequences on top of that.

Please keep following up on the soft tissue injuries even if they feel manageable right now. Neck and shoulder stuff from rear-end impacts can genuinely worsen over the first week or two as inflammation sets in. Keep a simple log — just notes on your phone about how you feel each day, what hurts, how it affects sleep or work. That record matters more than people realize later on.

I'm sorry you're dealing with this on top of actual physical pain. It's such a violation to be hit AND then get pressured to cover for the person who hit you. You sound like a genuinely decent person for even thinking about their situation, but please put yourself first here. You owe them nothing.

To answer your second question specifically — no, just receiving that message doesn't put you at risk. You haven't agreed to anything. But if you were to respond in a way that could be read as "going along with it," even vaguely, that gets complicated fast. Radio silence toward the other driver from here on out is the safest play. Route all communication through your insurer.