I've been there many times, but I've stayed at Long Point campground, a county park just up the road from Sebastian inlet SP, but unlike the SP most of the sites are right on the water with boat access.
Although I've fished there many times, I'd be the last person to give advice on what to do. :B
I would second the recommendation of the bait shop. It is just past the Long Point campground entrance road (north of the inlet)on A1A. It is, or at least was, called Whitey's, I think.
I believe you can get a license by calling or going online
Florida fishing license