Also, is it possible to run any kind of regression analysis using two different year's data for 2 different variables? for example: co2 emission data for 2019 and asthma prevalence data for 2018.
Sure, you could do this sort of thing. I think that your case for a causal relationship would be better served by using, say, 2018 data for CO2 emission, and 2019 data for asthma prevalence, however.
The question is, what is the smallest level at which you could collect reliable data for both variables? At the country level, a state level, a district/township/municipality level? The higher the level of aggregation, the greater the likelihood that observed relationships would not mirror very well what you would find if you had the luxury of tracking the two variables at the individual person level. Sociologists refer to this phenomenon as the ecological fallacy.
In Cincinnati there's an asthma group working on environmental pollution (diesel particles, esp) and asthma correlates. They might have better insight.
There is a direct correlation between temperature & carbon dioxide (CO2) in the atmosphere. Source of CO2 is primarily from using fossil fuel, breathing when exhale & plant decay. While living plant photosynthesis converts CO2 to oxygen, which equalized the creation of CO2 until we started using too much fossil fuel and paving & deforesting the countryside.
The additional CO2 in the atmosphere acts like a blanket that holds and absorbs some of the infrared radiation that normally leaves our atmosphere. Then the heated CO2 is released to space and the rest is pushed back to earth. This increases the temperature of the earth & its oceans. Warmer oceans & land have resulted in severe weather & forest fires.
So if we reduce CO2 emissions we reduce the CO2 pushed back to earth from the blanket and less heating up.
It would depend on what length of exposure to CO2 is required for subsequent development of diagnosed asthma. If it took many months, then this would argue for at least one year separation between the two variables. If only a few weeks, then data from the same year would likely be best.