ZJX Controller described a loss of separation event due in large part due to faulty communications between controllers at the same and adjacent sectors.

Narrative

I was working as a tracker for the St. Augustine; Sector (58) during the very busy day. My attention was divided by MCO spacing; a massive amount of overflights (including some very slow ones); and having to call Miami Center on every other hand off. The loss of separation happened while I was in the middle of a briefing. I tried to keep up with everything going on during the briefing; but I was exhausted at the end of my shift and missed one bad clearance. Aircraft X came over from the Keystone; Sector (76); at FL350. He was on the boundary with my sector and Green Cove (75). The point out was not made to 75 and we descended him through VNR164. We realized what happened when Aircraft X asked about the traffic at his one o'clock; and by then it was too late. We put up a 'j ring' and it looked like they were about 4.5 miles and 500ft. Recommendation; I think the problem came down to a breakdown of communication. In the future as a tracker; my goal is to improve on the communication with the team. This most likely would not have happened if we were all on the same page with everything.