I disagree with "Get a lawyer now." I agree, get her insurance information and report it. Also, your car insurance might cover this as well. Your insurance might cover it up front and then deal with the getting reimbursed from her later, depending on your state and policy. In many states this is called "no fault" "med pay" or "PIP" (Personal Injury Protection) coverage. (That way you wouldn't need to pay your high deductible first.)
Here's why I don't think you need a lawyer now. A lawyer will take about 1/3 of your settlement. If you have a bad accident and the insurance company is offering a really low amount, then a lawyer can really increase that offer and you end up with more in the end. But, the insurance company can only offer an amount up to the policy limits. If you are in California, where the "minimum limits" are like $15,000 a lawyer doesn't help you if that is the policy this person has. They just take $5,000 of that leaving you with $10,000. You can ask her about her policy when you get the police report. The insurance company usually can't tell you this without her permission. (If it is too low, then you could try to collect from her personally or from your own insurance "underinsured motorist" provision if you have that coverage. You probably would need a lawyer to do that.)
Any good lawyer will tell you to treat and get better. They would help you give your recorded statement, but not that much. They help: Tell the truth. Answer the question asked (no more, no less). Don't volunteer information. Don't try to be nice/ forgiving of the driver. Don't "take responsibility" that you don't truly believe is yours.
Once you get better, assuming that is within 6 months to 9 months, then negotiate with the insurance company on your own in a firm, professional, adult manner. Give them your medical records. Make a demand in dollars. See what happens. Then, if you aren't happy, get a lawyer. Yolfer is right that some insurance companies are harder to work with than others. You'll have that figured out within 2-3 months. If you don't resolve it within 9 months, talk to a lawyer about the statute of limitations in your state.
Usually, settlements are 1 to 3 times your "economic" damages. If you have $10,000 in meds, you can expect to get (in noneconomic damages) between $10,000 and $30,000. (Ballpark of course, there are always exceptions.) With a reasonable insurance company that offers you (as a first offer) $5,000, you could probably get them up to $10,000 + meds on your own. Add a lawyer, and you get $20,000 +meds . But the lawyer gets $10,000
(1/3 of $30,000 total). You still get $10,000 yourself. (And this is assuming that the driver has a policy that isn't the minimum, or your state has a minimum of more than $30,000.)
Of course, if the insurance company offers you $1,000 and won't go any higher than $5,000, or if they deny your claim outright, etc. getting a lawyer right away is a great idea. Don't wait longer than a year to get a lawyer.