Flight Instructor with student reported they possibly caused a NMAC during final approach.

Narrative

I was with my student south of ZZZ; when he said he smelled gas. He said it was bothering him and so I had him open the window and we decided to go immediately back home. I couldn't smell anything but didn't want to question if there was actual a leak. We made our calls into the pattern. There was an archer on the upwind leg but not anywhere in our vicinity. He made a 10 mile call; a 6 mile call; and the 45 call. He accidentally stepped on someone on the radios and said right pattern work and I told him to fix it. We turned onto our base quickly since he said it was bothering him again. I heard a woman's voice say she was base for XX (and we were halfway through base). My student said he was base to final for XX and we turned a bit prematurely. A man's voice said 'Are you aware that you just cut us off? You were within 200 feet of us.' I had checked final and it was completely clear. I never saw any aircraft on final; and did not see anyone on the left. I had no clue why they turned base if they did think we cut them off or why they waited so long to say something if we had. I was about to explain that I was only moving quickly because I thought we had a leak and I had no intention of cutting anyone off but it was just too busy and I couldn't get a word in. I sincerely hope that call wasn't for us. He never said any callsign of any sort; I assumed it was for us because it was for the same runway at ZZZ. I asked other people on the ground and they said they didn't hear any yelling at all. I don't know what happened or if he was talking to us. After we landed; a Cessna 172 landed and it was a female's voice again. There was an archer and a C-172 but I don't know who was talking to who.