Center Controller reported an airspace violation associated with presumed equipment issues.

Narrative

I was working the radar position at Sector XX without a D-side. Traffic volume was high and increasing throughout my time at [Sector] XX. At the time; I had numerous aircraft transitioning my airspace southwest bound requiring a point out or hand off to sector(s) XX; XY; and YY. In addition to the high traffic volume we had flow restrictions going into ZZZ that added to my workload. When I saw the PVD indicator in the data blocks of the aircraft transitioning my airspace southwest bound I assumed that Sector YX had a data block. I was correct on all but Aircraft Y; who was not PVD'd to YX for reasons unknown to me. Maybe I mistyped the sector number? I don't know. But I did not catch it because I was busy and did not verify that YX had accepted the Point Out by clicking on the PVD indicator or checking the URET (User Request Evaluation Tool).Ultimately; the data block popped at Sector XX's boundary and began flashing with Aircraft X who had been issued FL290. Aircraft X was climbing through FL240 at the time and the radar controller issued an amended altitude clearance of FL270. A traffic call was issued to both aircraft.Our staffing is not adequate to provide the support we need on position in the form of D-sides or trackers. We are not afforded enough break time in between being on position. We do not have enough CPC's to properly staff the area.Management and TMU (Traffic Management Unit) are not doing their jobs by slowing traffic down to manageable levels for the amount of staffing in the area.Our low staffing has also resulted in excessive overtime assignments in the area leading to burnout and/or work fatigue.