I agree with the others. Your claim is likely worth a few hundred in go-away money.
However, I once got rear-ended and got $700 with no doctor visits and $10 worth of Tylenol.
This is not legal advice. My many years in the insurance industry suggests the following.
Make sure you are fully recovered and pain free with no medication for at least two months to make sure there are no residual issues. Whiplash (soft tissue) aches and pains sometimes hide more serious issues so don't be in too much of a hurry to talk money.
When you are ready to talk money with the adjuster don't ask for an offer as you will be offered peanuts and there won't be much wiggle room. Ask for an amount. I know, you don't know what your claim is worth. Doesn't matter. Nobody ever gets what they "think" it's worth.
Don't ask for pie in the sky. You don't want to put your adjuster's back to the wall. And don't threaten lawsuit or lawyer because your adjuster will know darn well you won't follow through on such a small claim and no attorney is likely to take it on a contingency.
I'm not going to suggest a number.
You pick one and I'll tell you what I think of it from an adjuster's point of view.