Being sued for auto accident now wondering if limits are too low

Long story short, I caused an accident by being pulled out too far into an oncoming lane. The other driver was going about 40 when he hit my front bumper. The other driver initially appeared unharmed, but he ended up going to the hospital because he started to have head pain.

I am being sued for around $700k for medical bills, pain and suffering, loss of wages. My liability coverage for bodily injury is $250k, $140k of the claim is for medical bills the rest is pain and suffering/lost wages. My insurance has verified his claim and is going to offer policy limits. The other driver also has UIM that he is also suing.

To my understanding if the other driver accepts my insurance’s offer of policy limits then he can no longer come after me to obtain any additional money. It seems likely he will accept the $250k because I don’t have that kind of money laying around either in cash or in assets aside from my home which I only own about 15% of the equity.
This has gotten me thinking though should I be carrying more insurance? My agent said 250k is a lot more than lots of people have, but even though this accident did not leave anyone bleeding and crippled, it exceeded policy limits anyways because he required surgery. Makes me wonder what happens to people that carry the minimum and injure a whole family of people? I thought 250k was a responsible amount to carry and am feeling very bad that I have caused so much harm to this person that I don’t have insurance to pay for.