An elderly woman pulled out in from of me, I swerved hard, missed her and hit a tree.

This is not a no-fault accident.  Pennsylvania has "no-fault" insurance for medical coverage which means that your insurance company pays "PIP" or first party coverage for your medical treatment until your policy limits are exhausted.  However, just because medical treatment is covered by each party's own insurer regardless of fault, that doesn't mean that the driver who is at fault is not liable for property damage, pain and suffering, or medical expenses over the first party insurance limits.  In this case it sounds to me like the woman would clearly be found to be at fault.  You should contact a qualified Pennsylvania Car Accident Lawyer and you should probably review the information at: http://fairlielaw.net/practice-areas/car-accidents/