A320 flight crew reported a fumes event during arrival taxi which was different from any other fumes the flight crew had experienced previously. Flight crew and a Flight Attendant reported 'brain fog;' headaches; and sore throat symptoms. Maintenance could not duplicate the issue.

Narrative

During our taxi to the gate in ZZZ; we received an AIR PACK 1 REG FAULT ECAM. We followed ECAM followed by the X procedure. Shortly thereafter; we turned the APU BLEED on when we entered the ramp area for our tow into the gate. We immediately smelled some sort of odor neither of us have ever experienced before. Having had fume events in the past; and all of them having the same smell; that of a dirty sock or gym locker room; this was a different smell. I immediately turned off the APU BLEED and at the same time; the lead FA called the flight deck and said she smelled an odor as well. The FO and I also opened up our cockpit window. There was no more evidence of the odor and we were towed into the gate.The FO called Operations to have them send maintenance out to meet us at the gate. We described everything and I asked if I should fill out the fumes/odor report; they said it wasn't necessary. I don't know why I questioned it; I should have filled it out. I am now deeming this situation as a possible fume event. Our configuration was both engines OFF; APU BLEED ON. The odor smelled like a burning chemical. In my past experience with fume events; my typical symptoms were sore throat; itchy eyes and the following day I feel as if I had brain fog. I didn't experience any of these immediate symptoms; which is why I initially disregarded it as a fume event. The next morning; the FO and I both had headaches. Later that afternoon; I started to feel like I had brain fog and not being able to think clear and a sore/scratchy throat. I received a text from one of the flight attends the same afternoon saying she didn't feel well all day and her text also said some of the passengers in the front of the cabin were coughing. That was the first time I heard about the passengers.When we arrived at the airplane in ZZZ the following day; I spoke with the mechanics from the previous evening. I asked what happened with the aircraft and they told me they 'could not duplicate the smell.' I asked Maintenance Control if that aircraft had any follow up write ups regarding the same ECAM or any fume events since; and there were none.I looked back at the whole situation and decided that it is best to write a fumes report as well as an safety report.