How do I go about this situation? Can they really fire me?

You need to apply for Interminttent Family Leave until they give it to you. This way you can not be disciplined for taking the occasional day off. Dont worry about your meeting. They may just need to discuss whats going on, They are most likely going to figure out a plan and lay everything out on the table. They CAN NOT fire you for that, its illegal. I doubt they will try it. Sounds like you are a lot better than the place you work for. Some people can be heartless. Good luck, I wish you lots of health.