From the description of the accident with other lady driver at the guard shack in Rhode Island it would sound as if she was at fault and thus you would put a claim through her property damage liability coverage.
If you were somehow unable to get her information or she did not have insurance for you to put your claim through then you could put a claim through your own collision coverage.
Insurance companies rating systems differ so you would have to find out from your agent if this not at fault accident and/or claim you may place through your own insurance policy will affect your insurance premiums.
The Rhode Island Insurance Division of the Department of Business Regulation notes that drivers with violations or at-fault accidents are considered to be a higher risk and may be charged a higher rate. They do not mention not at fault accidents causing higher premiums so it likely depends upon your insurance carrier's rating system, which must be filed with this state insurance regulatory body of RI.
If your rates do rise due to this unfortunate accident or due to other reasons, you can get a quote for inexpensive car insurance here with us.