How do I compare coefficients from my glm when I have more than one factor variable in my formula?
R chooses the baseline level by itself unless you specify it. You can read here how to specify it: 
https://stackoverflow.com/questions/3872070/how-to-force-r-to-use-a-specified-factor-level-as-reference-in-a-regression

Then you can change the reference (baseline) level to get all the possible results. This is easy to do but I am not sure if it is the best way to go, since you need to repeat yourself many times. But I think this might be better if you could apply it on your own data:

https://stats.stackexchange.com/questions/60352/comparing-levels-of-factors-after-a-glm-in-r

This is the link to the R package documentation: 
https://cran.r-project.org/web/packages/multcomp/multcomp.pdf