ZID Controller experienced a loss of separation event during a heavy/complex traffic session with multiple weather deviations; the report acknowledging distractions from flight plan updates contributed to the conflict.

Narrative

I was working a complex busy session of traffic at a high altitude RADAR sector. Nearly 100% of the aircraft flying through my sector were either deviating or terminating deviations. This is very time consuming and labor intensive. I had my hands full and was utilizing my D-Side during this session. One of our low altitude sectors was getting impacted by a high volume of aircraft heading to a fly in event causing a last minute explosion of volume. They needed to split a sector from that position which caused the Supervisor to take my D-Side to open the new sector. I was stunned when my D-Side left; then I turned and saw why he was leaving and it made sense to me because of the need to open a new sector. I felt like I needed some help but figured someone was coming soon so I continued to work the complex sector. Air Carrier Y had started talking to me about starting a turn toward SPI at this time but wasn't done deviating left and that maybe deviating direct to MCI would be better for them. I began updating the flight plan and clearing the aircraft to deviate for a second time and got wrapped up in the task and didn't notice that Air Carrier Y was turning right toward another aircraft to the right. Since I was in back and forth transmissions with Air Carrier Y; I descended them to FL350 as soon as conflict alert activated. I then told Air Carrier X to fly heading 310; which was about 50 degrees to the left of course; then gave Air Carrier Y a 20 degree left turn; this resulted in the 2 flights moving away from each other. Air Carrier Y called the traffic insight. Recommendation; be aware of deviations and don't get caught up in the paper work.