Contact a personal injury lawyer ASAP. You need to file your no-fault insurance claim form on your carrier within 30 days of the accident to get your medical bill and lost wages paid. You can seek pain and suffering damages from the woman you hit you if you show you suffered "serious injury" as that term in defined in the Insurance Law. Surgery alone is not "serious injury" but could be depending on how things turn out.
It is because of the composition of the jury pool. The jurors in Westchester are mostly property owners who are very conservative whereas the jurors a few miles a way in the Bronx are mostly members of a minority group, more likely to be renters, and far more liberal in awarding damages. A mediation requires both sides to agree. If you do not like the offer you can always proceed to trial.