What fallacy does argument commit ?

As there were a number of reasons from the outset I didn't believe in a novel virus or pandemic I did what I believed was my responsibility as a citizen to stand against authority and not comply with all rules as much as I was able, including not wearing a mask, so I was often the only person in the train carriage, the only person in the supermarket, the only person on the plane, the only person in the doctor's waiting room not wearing a mask - that aspect worried me only minimally, what concerned me more was being forced to comply in order to do or get something I felt I really needed. I ended up incurring two hefty fines which I'd planned on fighting in court but paid instead, however, I have no regrets.

These are the two guideposts and two fundamental rules of critical thinking I follow to come to conclusions about the truth of things which I also followed to come to my conclusions about the pandemic. I've written a three-part article, Critical thinking: The moon landings, 9/11 and covid. The third part is Part 3:  The second fundamental rule of critical thinking applied to covid.

THE TWO GUIDEPOSTS
1. Every relevant piece of information will at least support if not favour the correct hypothesis
It is useful to constantly bear in mind that the nature of reality is that every single relevant piece of information will at least support if not favour the correct hypothesis. Any relevant item selected at random will show that it at least is consistent with the hypothesis if not favour it. If not, the hypothesis isn’t correct. Sometimes seeming anomalies might contradict the correct hypothesis but on closer inspection will be revealed to be only seeming anomalies not real anomalies.

2. Internal consistency and consistency with expectations
Where all the evidence is both internally consistent and consistent with expectations, unless a good reason is put forward for doubt we should accept an hypothesis as correct.

THE TWO FUNDAMENTAL RULES
Rule 1: Aim to prove your hypothesis wrong
When I came across the statement by Kary Mullis, the Nobel-prize winning inventor of the PCR technique, in an interview with Gary Null, "The scientist aims to prove their hypothesis wrong," I thought, "Bingo! That's what I do.” If ever what I believe is challenged by anyone or anything I review my hypothesis against the challenge to see if it still holds. I also go out of my way to investigate the opposing arguments sufficiently to ensure I can respond to them … and if I can’t respond with a good argument, I change my mind or at least “park” the challenge for later review. Richard Feynman effectively said the same thing as Kary Mullis in his commencement address at Caltech in 1974 entitled, Cargo Cult Science.

Rule 2: Confine your analysis to the most relevant and unarguable-with data in the first instance
If the nature of reality is that every single piece of evidence will at least support if not favour the correct hypothesis then if there is a reasonable amount of unarguable-with data and all of it supports your hypothesis if not favours it over any other then it's going to be rather difficult for another hypothesis to be correct.

Following my Rule 2 of confining analysis to the most relevant and unarguable-with data in the first instance we can only conclude there is no novel virus, no pandemic and no requirement for a jab. However, I always follow my Rule 1 - so happy to be proved wrong!

If you believe in the pandemic I wonder what rules of critical thinking you use to come to that belief.

Would saying that this argument commits the ad populum fallacy be correct? because they're using the reason that other people aren't wearing masks as the reason, they're also deciding not to wear them?

I did not see that as a fit because the conclusion wasn't that wearing masks were "good/bad" or "right/wrong", but that it was "required." Again, seeing nobody wear masks is a good indicator that masks are not required/needed.

The jump from “I don't have to …” to “(I) shouldn't be punished …” seems like quite a leap!  At best, it’s a non sequitur .

To improve the argument, clarification of what is meant is needed.  Leaving the other party to make guesses or assumptions about what we mean is problematic.  It can also be deceitful if followed up by switching the meaning during the exchange.

Well, I said "I think" (not 100% sure). People don't always express themselves accurately. They mean something and express it in a way that can have a few to many different interpretations. "I don't have to do something" a lot of times means that "noone is making me do something". "Have to" means obligation. Either from a person or a physical situation. It seemed to me too stupid to have any other meaning than that of being forced by someone. For example, the only other interpretation I can think of what "I don't HAVE TO" would mean is "I am not at risk of getting sick from COVID, (thus I don't HAVE TO wear a mask) because nobody is wearing" which is not just non-sequitur, it's just plain stupid. That's why my comment addressed only the first case. So, I don't think it was actually "quite a leap", as you say.

We seem to be in agreement that arguments need clearly-defined and mutually understood meanings of the terms and concepts presented.  Without that common understanding (and the associated need for perhaps unstated assumptions), we risk (at the best) talking at cross purposes and (on a worse level) having an unscrupulous party intentionally misleading by switching meanings mid-discussion.

In that, we indeed agree!