Does a concern and deep desire to reach lost souls with the gospel and a desire to see others saved a good indication of the Holy Spirit at work in ones life?
Yes. Once you yourself are saved, it’s logical for you to want friends, loved ones, and even total strangers to experience the wonderful feelings of freedom and joy that come with being saved.
You can be sure that this is the Holy Spirit at work within you. He wants all people to be saved even more than you do (2 Peter 3:9).