I am the only woman player in my area. Can I still be a part of the event?

Yes, if there are no local tournaments, you might consider sanctioning and running your own WGE tournament. You will need to complete a sanctioning agreement and meet all sanctioning requirements (current membership, certified official, fee payment) and all WGE tournament requirements (3 propagators on the same layout, upload scores, submission of TD Report. etc.).

Check out the PDGA Tour Event Planning & Management resources for more information on running a tournament.