Assuming the current scientific orthodoxy on global warming is correct (and this is not the place to debate that question - I'm only noting here that in science all orthodoxies must be open to sceptical challenge), there certainly is an argument that you bear something on the order of a billionth of the responsibility for the consequences. It's not zero. But matters of causality on this fine a scale are never so simple.
There is the direct effect of the emissions, there is the effect on prices, there is the effect on political opinions, there are opportunity costs and paths not followed. There are major questions of what people would do instead, if they were not working in the holiday industry. Suppose we argue that it is all the people going on holiday that spurs political action. Suppose instead of going on holiday you spend your money on other luxuries, the manufacture of which polluted more. Suppose we argue that if the people of developing nations were not being paid by tourists, they would instead have to make their livelihoods in factories that pollute more heavily. There is a vast network of causes and effects, and it is impossible to trace the cumulative net effect of any individual action. And when you are talking in billionths, such effects become significant.
There is also a range of possible solutions and trade-offs that one might support. One obvious option is for the world's energy generation to go nuclear, as France did in the 1980s. Another is to develop the economies of vulnerable nations so they have the resources to adapt to climate change. Or to offset, or distribute the costs differently, or to compensate victims for their losses, or to pay the costs later, when the world is richer. There are many possibilities besides simplistic prevention-through-austerity, and if you are a believer in one of the alternatives that doesn't require you to stop travelling by air, but solves the problem a different way, then you may argue that you see no moral duty to be part of this particular solution.
There is also a major theme of political philosophy here, which is the historical phenomenon of political movements using forecasts of imminent disaster to demand their desired political changes be rushed through without proper debate or scrutiny, because it is an emergency. As H L Mencken put it: "The whole aim of practical politics is to keep the populace alarmed (and hence clamorous to be led to safety) by menacing it with an endless series of hobgoblins, all of them imaginary." Thus, for every emergency situation demanding urgent political action, we need to have a rigorous process in place to determine whether this is indeed a real emergency, or just another hobgoblin. (Again, not commenting on whether it is or isn't in this case - just noting the general phenomenon.) Because you see there is a risk on the other side of the balance sheet - that if this were a false alarm like the 'Population Bomb/Limits to Growth' stories of the 1960s and 70s predicting imminent global doom ("Demographers agree almost unanimously on the following grim timetable: by 1975 widespread famines will begin in India; these will spread by 1990 to include all of India, Pakistan, China and the Near East, Africa. By the year 2000, or conceivably sooner, South and Central America will exist under famine conditions….By the year 2000, thirty years from now, the entire world, with the exception of Western Europe, North America, and Australia, will be in famine." "If I were a gambler, I would take even money that England will not exist in the year 2000" etc.), then any actions taken to support the scare might have serious global repercussions for freedom, democracy, and economic development. Sterilisation of the poor in exchange for aid, and China's 'one child' policy followed the overpopulation scare, which were a particularly horrific moral cost of believing uncritically.
A lot of developing nations rely on Western tourism for a big part of their economy. Taking that away by shutting down air travel is a risk that should not be ignored. In deciding not to fly abroad for a holiday, you take on some billionths of the responsibility for that, too.
So another part of the moral action we all need to be responsible for is to make sure forecasts of disaster and demands for urgent political action are examined rigorously, to distinguish the many imaginary hobgoblins from the occasional real ones. Warning signs should be taken seriously - like supporting data being hidden, numbers being 'adjusted' or 'made up', sceptical challenge being suppressed, opposing arguments being silenced. Sceptics are an essential part of the process of building scientific confidence. Data transparency, quality audits, software quality, scientific replicability, multiple layers of checking and reanalysis should be the order of the day in trillion-dollar decisions. Not because we don't want to believe, or want to delay action, but to generate the quality of evidence we need to safely act when it is essential, and not waste all our resources on costly false alarms, or cause even worse moral harm needlessly.
Whether we believe the current scientific orthodoxy to be true or false, we should all agree that on end-of-the-world questions it should be proven to be of the best possible quality.
You are balancing potential harm due to climate change against potential harm to the economic development of poorer nations. There is no morally safe answer. Your individual responsibility is small but probably not-zero, so perhaps the best thing you can do, if you are worried, is encourage open debate, so that we can collectively make the best decision on the best evidence.