Received a pain and suffering offer of $4k after my car accident. Is that reasonable? (KS)

I was in a car accident on January 29th of this year, in which I was rear ended by an elderly woman going about 40mph. My car was totaled, and I suffered a concussion and 2 bulging discs in my neck. The other party's insurance accepted complete liability, and compensated me for my car, and paid all associated medical bills. I spent 78 days "treating" before hitting max expected recovery.

The first month was absolutely awful, with the worst of it setting in a few days after the accident. I was unable to support the weight of my own head and was pretty much confined to staying in bed. For about a week I existed in a state of constant motion sickness and it was one of the most unpleasant experiences of my life. I finally got better after a course of steroids and pain killers/muscle relaxers. I rested, saw a specialist, and toward the start of April, I felt I was pretty much back to normal. There are some things that cause my neck to occasionally flare up, so I have to be more conscious of my posture and certain activities now, but that's just how it is going to be. In a clinical sense, I do not have any long term injuries, and since I'm in my mid-20s, I've been assured that I'll heal up just fine over time, but it will be a potential weak spot in the future.

I am on Medicaid, and my health insurance company negotiated down my various bills, including a CT, X-ray, and MRI. All in all, there is only about $850 in medical bills. The other party's insurance will be reimbursing Medicaid for that amount. I spoke with the medical adjuster today, and they offered me $4k for pain and suffering. I told him I would think about it, and he replied, "Well we have some wiggle room, so let me know what you have in mind."

I have no frame of reference for this scenario. Is $4k reasonable for the injuries I suffered? In hindsight, it was a very frustrating 2 months. I work with my hands, and I'm an avid outdoor/adventurer type. My wife and I bought a house and got married last October, and I had to stop all home renovations. I couldn't garden, take my dog on hikes, ride my bike, go golfing, etc. What would a reasonable counter offer be if $4k is low? The state minimum in KS is $25k for bodily injury, and since they only have to pay less than $1k in medical bills, there's quite a bit of room on the coverage. Initially, I was going to ask for $6k, but everyone I've spoken to has told me that is much too low, and I need to try to get at least $10k, if not $15k. Personally, I'd be nervous asking for that much since it is so much higher than their initial offer. They have also been incredibly accommodating throughout this entire process, so I don't want to seem like a greedy jerk.