Center Controller reported a VFR aircraft unexpectedly turned into the path of a climbing air carrier resulting in a NMAC.

Narrative

I was working the R-Side at Sector X without a D-side; when Aircraft X departed on the ZZZZZ Departure out of ZZZ. I received a point out from Sector Y on Aircraft Y; a VFR that was doing airwork within an estimated 40 mile radius around ZZZ at 16;500 ft. There was no paperwork at any sectors for the airwork that this aircraft was doing. I am unsure whether this airwork was even cleared with TMU (Traffic Management Unit) prior to this operation. It is an extremely dangerous area for this aircraft to be operating; because of the impact it has on all of the departures and arrivals into and out of ZZZ. When Aircraft X initially called me up; I climbed him to 34;000 ft. and put the aircraft on a 200 heading. This heading would have separated him from Aircraft Y based on his projected course west bound. After I put Aircraft X on a heading; I received a call from ZZZ1 for a handoff on Aircraft Z; who had exited the warning area. I was struggling to get Aircraft Z tagged up and flight plan information put in; when Aircraft X transmitted on the frequency that he was responding to a TCAS RA.I redirected my attention to Aircraft X; and Aircraft Y had completely reversed his course East Bound; right into Aircraft X course. I did not have time to issue traffic or a traffic alert. I was very flustered when this happened and I told Aircraft X to stop his climb. I understand that I should not have issued a control instruction once the aircraft stated that they were responding to a TCAS RA. Aircraft X descended back down to 14;000 ft. in response to their RA. I believe these two aircraft were within 300 ft of each other. I immediately asked the supervisor for a D-side as the traffic volume was very high and complex and I still was not able to get Aircraft Z tagged up out of the warning area. In hindsight; I understand that I should not have climbed Aircraft X; even if I vectored him to avoid the VFR; if I did not have time to monitor the situation; because the VFR aircraft could unpredictably reverse course.I also understand that I should have issued a traffic alert. Additionally; a few minutes later; Aircraft X was over ZZZ2 climbing out of 26;000 ft. for 30;000 ft. My D-side received a call from Sector Z; that they had a flight of 2 at 27;000 ft. headed north bound that was a direct conflict with the Aircraft X; and they were not talking to the flight of aircraft. Sector A had failed to transfer communications to Sector Z; so I had to turn Aircraft X aggressively to miss Aircraft A. There was no loss of separation on this second incident; but it was extremely unsafe and undoubtedly it made the pilots on Aircraft X feel very uneasy.I believe that if I had a D-side during this event; I would not have missed Aircraft Y reversing course and heading towards Aircraft X. My D-side would have been able to take the call from Sector A for the Aircraft Z and I would have been able to focus on separating traffic. I would recommend that any time the warning area is active during the months of May to September (busiest traffic periods) that we staff a D-side at Sector X. One of the reasons that we do not always staff a D-side at Sector X is because we do not have enough staffing to safely run the operation in the summer. Our staffing numbers for the day and night shifts have been negotiated at 10 people. This number is not sufficient to split sectors and staff a D-side; even when it is needed.