Enroute Controller described an airspace deviation when the D-Side was replaced during a very busy and complex traffic period.

Narrative

As I returned from break our supervisor asked me to take over as D-Side for some one who is certified at that position and was already working the red sector. I then got in position and tried to catch up on what was going on. I called an adjacent sector to slow departures and no answer. I called them again to get communications of another aircraft and had them ask about a manual IFR hand off. At this time the RADAR Controller asked me to get communications of another aircraft and another sector popped in my head to try and help by telling me he would take an aircraft to the North into his airspace. The adjacent facility controller then ask me if Aircraft X was RADAR and I asked were he was at. I started track and and told the RADAR Controller to have him IDENT to make sure he was the right primary. I was unaware of the second manual hand off of Aircraft Y. The tracks started on the wrong beacon codes and Aircraft Y entered an adjacent sector without being handed off. Recommendation; not to put in a new controller when the sector is already red and the controllers involved already have a good picture of whats going on. Also a tracker should have been added to the position; instead of a supervisor just standing off the shoulder watching not plugged in and not saying anything.