Can I receive unemployment for being fired due to illness?

Question Details:

I called out of work last year on several occasions, I have a 4 year-old child and he has been sick, as well as I had 2 miscarriages. I was given a verbal warning and 2 written warnings because I used all of my paid time off. This year I called out once for a total of 4 days due to extreme high blood pressure. I have paid time off but still received a warning that if I call out again I will be fired. I have doctors notes for almost all the days that I took of. I was wondering if I can receive unemployment in NY if I do get fired? Important Notice