I guess when you keep using loaded words with negative connotations like "alibi" and "sadly", it is not easy to believe that you want to actually do a research paper - it seems like you want to do an opinion piece and support your arguments with research. There's nothing wrong with that, per se, but it isn't a "research paper" in any meaningful sense. But I'm probably being too pedantic, so my apologies, as I should be more helpful.
It looks like you are comparing two relationships:
1. The relationship between cigarette taxes and health.
2. The relationship between cigarette taxes and government revenue.
First you need to define and explain your terms.
What is your population? Who are you studying? What are the boundaries of your investigation? A country, a city, a province? This will probably be determined by how detailed of data you can obtain - and it may only be nationally available.
What is a cigarette tax? How is it calculated (as a percent of the value of a pack of cigarettes or a the same amount for each pack)? What was the tax on a year to year basis going back as far as you need to? This will give you your first set of numbers. Is the amount of the tax really what you need to look at (when looking to health) or is it the impact of the tax on smoking rates?
What do you mean by health and how do you measure it? I would think for your paper, you should limit "health" to diseases or problems "known" to be caused by cigarette smoking. Or maybe you can, for simplicity's sake, just pick one disease, such as lung cancer. Then how will you measure health? Disease rates? Healthcare costs? Also, assuming for the sake of argument that increases in the cost of cigarettes decrease usage (another point you need to address, which may be resolved using supply-demand curves) and that decrease in cigarette usage improves health, improved health will be a "lagging indicator" for chronic smoking-related diseases - this means that the decrease in tax will not cause an immediate improvement in health of the population.
I'm going to stop here because I have no idea whether this is helpful for you. If so, I will try to write some more. Good luck with your paper!